2x^2-15+4x^2-2x^2=180

Solution for 2x^2-15+4x^2-2x^2=180 equation:

2x^2-15+4x^2-2x^2=180

We move all terms to the left:

2x^2-15+4x^2-2x^2-(180)=0

We add all the numbers together, and all the variables

4x^2-195=0

a = 4; b = 0; c = -195;
Δ = b2-4ac
Δ = 02-4·4·(-195)
Δ = 3120
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:

$\sqrt{\Delta}=\sqrt{3120}=\sqrt{16*195}=\sqrt{16}*\sqrt{195}=4\sqrt{195}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{195}}{2*4}=\frac{0-4\sqrt{195}}{8}
=-\frac{4\sqrt{195}}{8}
=-\frac{\sqrt{195}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{195}}{2*4}=\frac{0+4\sqrt{195}}{8}
=\frac{4\sqrt{195}}{8}
=\frac{\sqrt{195}}{2}
$