5x+5x^2=50

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

5x+5x^2=50

We move all terms to the left:

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

a = 5; b = 5; c = -50;
Δ = b2-4ac
Δ = 52-4·5·(-50)
Δ = 1025
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:

$\sqrt{\Delta}=\sqrt{1025}=\sqrt{25*41}=\sqrt{25}*\sqrt{41}=5\sqrt{41}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-5\sqrt{41}}{2*5}=\frac{-5-5\sqrt{41}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+5\sqrt{41}}{2*5}=\frac{-5+5\sqrt{41}}{10}
$