50=25x+5x^2

Solution for 50=25x+5x^2 equation:

50=25x+5x^2

We move all terms to the left:

50-(25x+5x^2)=0

We get rid of parentheses

-5x^2-25x+50=0

a = -5; b = -25; c = +50;
Δ = b2-4ac
Δ = -252-4·(-5)·50
Δ = 1625
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:

$\sqrt{\Delta}=\sqrt{1625}=\sqrt{25*65}=\sqrt{25}*\sqrt{65}=5\sqrt{65}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-25)-5\sqrt{65}}{2*-5}=\frac{25-5\sqrt{65}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-25)+5\sqrt{65}}{2*-5}=\frac{25+5\sqrt{65}}{-10}
$