2x^2=50x+150

Solution for 2x^2=50x+150 equation:

2x^2=50x+150

We move all terms to the left:

2x^2-(50x+150)=0

We get rid of parentheses

2x^2-50x-150=0

a = 2; b = -50; c = -150;
Δ = b2-4ac
Δ = -502-4·2·(-150)
Δ = 3700
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:

$\sqrt{\Delta}=\sqrt{3700}=\sqrt{100*37}=\sqrt{100}*\sqrt{37}=10\sqrt{37}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-50)-10\sqrt{37}}{2*2}=\frac{50-10\sqrt{37}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-50)+10\sqrt{37}}{2*2}=\frac{50+10\sqrt{37}}{4}
$