2x^2-5x+16+2x^2+5x-24=180

Solution for 2x^2-5x+16+2x^2+5x-24=180 equation:

2x^2-5x+16+2x^2+5x-24=180

We move all terms to the left:

2x^2-5x+16+2x^2+5x-24-(180)=0

We add all the numbers together, and all the variables

4x^2-188=0

a = 4; b = 0; c = -188;
Δ = b2-4ac
Δ = 02-4·4·(-188)
Δ = 3008
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:

$\sqrt{\Delta}=\sqrt{3008}=\sqrt{64*47}=\sqrt{64}*\sqrt{47}=8\sqrt{47}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{47}}{2*4}=\frac{0-8\sqrt{47}}{8}
=-\frac{8\sqrt{47}}{8}
=-\sqrt{47}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{47}}{2*4}=\frac{0+8\sqrt{47}}{8}
=\frac{8\sqrt{47}}{8}
=\sqrt{47}
$