9x+118=4x^2+80x+400

Solution for 9x+118=4x^2+80x+400 equation:

9x+118=4x^2+80x+400

We move all terms to the left:

9x+118-(4x^2+80x+400)=0

We get rid of parentheses

-4x^2+9x-80x-400+118=0

We add all the numbers together, and all the variables

-4x^2-71x-282=0

a = -4; b = -71; c = -282;
Δ = b2-4ac
Δ = -712-4·(-4)·(-282)
Δ = 529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{529}=23$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-71)-23}{2*-4}=\frac{48}{-8}
=-6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-71)+23}{2*-4}=\frac{94}{-8}
=-11+3/4
$