2x^2-50=75-3x^2

Solution for 2x^2-50=75-3x^2 equation:

2x^2-50=75-3x^2

We move all terms to the left:

2x^2-50-(75-3x^2)=0

We get rid of parentheses

2x^2+3x^2-75-50=0

We add all the numbers together, and all the variables

5x^2-125=0

a = 5; b = 0; c = -125;
Δ = b2-4ac
Δ = 02-4·5·(-125)
Δ = 2500
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2500}=50$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-50}{2*5}=\frac{-50}{10}
=-5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+50}{2*5}=\frac{50}{10}
=5
$