Question 146050
2x+3=4x^2
:
You can rearrange this is the quadratic form:
4x^2 - 2x - 3 = 0
:
Use the quadratic formula: 
{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}} 
In your problem: a=4; b=-2; c=-3
{{{x = ((-2) +- sqrt( -2^2-4*4*-3 ))/(2*4) }}}
:
{{{x = (2 +- sqrt(4 - (-48) ))/(8) }}} 
{{{x = (2 +- sqrt(4 + 48))/(8) }}} 
{{{x = (2 +- sqrt(52 ))/(8) }}}
Two solutions:
{{{x = (2 + 7.211)/8}}}
{{{x = (9.211)/8}}} 
x = 1.151
and
{{{x = (2 - 7.211)/8}}}
{{{x = (-5.211)/8}}} 
x = -.651