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

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

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

We move all terms to the left:

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

5x^2-75x-50=0

a = 5; b = -75; c = -50;
Δ = b2-4ac
Δ = -752-4·5·(-50)
Δ = 6625
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:

$\sqrt{\Delta}=\sqrt{6625}=\sqrt{25*265}=\sqrt{25}*\sqrt{265}=5\sqrt{265}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-75)-5\sqrt{265}}{2*5}=\frac{75-5\sqrt{265}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-75)+5\sqrt{265}}{2*5}=\frac{75+5\sqrt{265}}{10}
$