5x(2x+10)=50

Solution for 5x(2x+10)=50 equation:

5x(2x+10)=50

We move all terms to the left:

5x(2x+10)-(50)=0

We multiply parentheses

10x^2+50x-50=0

a = 10; b = 50; c = -50;
Δ = b2-4ac
Δ = 502-4·10·(-50)
Δ = 4500
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:

$\sqrt{\Delta}=\sqrt{4500}=\sqrt{900*5}=\sqrt{900}*\sqrt{5}=30\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(50)-30\sqrt{5}}{2*10}=\frac{-50-30\sqrt{5}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(50)+30\sqrt{5}}{2*10}=\frac{-50+30\sqrt{5}}{20}
$