SOLUTION: Solve: 3 over 2x-3 minus 5 over x = 1

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3 over 2x-3 minus 5 over x = 1
3%2F%282x-3%29+-+5%2Fx+=+1

Start by multiplying both sides by a common denominator x(2x-3):
.
x%282x-3%29%283%2F%282x-3%29+-+5%2Fx%29+=+x%282x-3%29%281%29

.
This results in:
3x+-+5%282x-3%29+=+x%282x-3%29

Solve for 'x' using the quadratic equation yields:
x = {1.915, -3.915}
.
Below are the details of the quadratic:

Solved by pluggable solver: SOLVE quadratic equation with variable

Quadratic equation ax%5E2%2Bbx%2Bc=0

(in our case 2x%5E2%2B4x%2B-15+=+0

) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac

should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac

.

Discriminant d=136 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-4%2B-sqrt%28+136+%29%29%2F2%5Ca

x%5B1%5D+=+%28-%284%29%2Bsqrt%28+136+%29%29%2F2%5C2+=+1.91547594742265

x%5B2%5D+=+%28-%284%29-sqrt%28+136+%29%29%2F2%5C2+=+-3.91547594742265

Quadratic expression 2x%5E2%2B4x%2B-15

can be factored:
2x%5E2%2B4x%2B-15+=+2%28x-1.91547594742265%29%2A%28x--3.91547594742265%29

Again, the answer is: 1.91547594742265, -3.91547594742265. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+2%2Ax%5E2%2B4%2Ax%2B-15+%29