2(2x^2-25x)+2(3x^2+60)=180

Solution for 2(2x^2-25x)+2(3x^2+60)=180 equation:

2(2x^2-25x)+2(3x^2+60)=180

We move all terms to the left:

2(2x^2-25x)+2(3x^2+60)-(180)=0

We multiply parentheses

4x^2+6x^2-50x+120-180=0

We add all the numbers together, and all the variables

10x^2-50x-60=0

a = 10; b = -50; c = -60;
Δ = b2-4ac
Δ = -502-4·10·(-60)
Δ = 4900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4900}=70$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-50)-70}{2*10}=\frac{-20}{20}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-50)+70}{2*10}=\frac{120}{20}
=6
$