Question 152786
Any time we only have one variable, we only need one equation to solve it. We know that the sum of the two halves of the line equals the whole line. Therefore:
{{{highlight(7x-2 + 3x+7) = 4x^2 + 3x + 2}}}
{{{10x+5 = 4x^2 + 3x + 2}}}
{{{10x + 5 - highlight(10x) - highlight(5) = 4x^2 + 3x*highlight(-10x) + 2*highlight(-5)}}}
{{{0 = 4x^2 - 7x - 3}}}
<br>This can't be solved by factoring. Instead, we can use the quadratic formula. 
{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}
<br>We know that in an equation ax<sup>2</sup> + bx + c:
{{{a = 4}}}
{{{b = -7}}}
{{{c = -3}}}
<br>Let's plug in the numbers:
{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}
{{{x = (-(-7) +- sqrt( (-7)^2-4*4*(-3) ))/(2*4) }}}
{{{x = (highlight(-(-7)) +- sqrt( highlight((-7)^2)-highlight(4*4*(-3)) ))/highlight(2*4)}}}
{{{x = (7 +- sqrt( 49-(-48) ))/8 }}}
{{{x = (7 +- sqrt(highlight(49-(-48))))/8 }}}
{{{x = 7 +- sqrt(97)/8}}}