2x^2+11x=-x^2+5x+88

Solution for 2x^2+11x=-x^2+5x+88 equation:

2x^2+11x=-x^2+5x+88

We move all terms to the left:

2x^2+11x-(-x^2+5x+88)=0

We get rid of parentheses

2x^2+x^2-5x+11x-88=0

We add all the numbers together, and all the variables

3x^2+6x-88=0

a = 3; b = 6; c = -88;
Δ = b2-4ac
Δ = 62-4·3·(-88)
Δ = 1092
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1092}=\sqrt{4*273}=\sqrt{4}*\sqrt{273}=2\sqrt{273}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{273}}{2*3}=\frac{-6-2\sqrt{273}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{273}}{2*3}=\frac{-6+2\sqrt{273}}{6}
$