3x-2x^2-12+8x-5x^2+1x+15x+3=2x^2-23x-87

Solution for 3x-2x^2-12+8x-5x^2+1x+15x+3=2x^2-23x-87 equation:

3x-2x^2-12+8x-5x^2+1x+15x+3=2x^2-23x-87

We move all terms to the left:

3x-2x^2-12+8x-5x^2+1x+15x+3-(2x^2-23x-87)=0

We add all the numbers together, and all the variables

-7x^2+27x-(2x^2-23x-87)-9=0

We get rid of parentheses

-7x^2-2x^2+27x+23x+87-9=0

We add all the numbers together, and all the variables

-9x^2+50x+78=0

a = -9; b = 50; c = +78;
Δ = b2-4ac
Δ = 502-4·(-9)·78
Δ = 5308
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:

$\sqrt{\Delta}=\sqrt{5308}=\sqrt{4*1327}=\sqrt{4}*\sqrt{1327}=2\sqrt{1327}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(50)-2\sqrt{1327}}{2*-9}=\frac{-50-2\sqrt{1327}}{-18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(50)+2\sqrt{1327}}{2*-9}=\frac{-50+2\sqrt{1327}}{-18}
$