5x(5x+10)=10

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

5x(5x+10)=10

We move all terms to the left:

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

We multiply parentheses

25x^2+50x-10=0

a = 25; b = 50; c = -10;
Δ = b2-4ac
Δ = 502-4·25·(-10)
Δ = 3500
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:

$\sqrt{\Delta}=\sqrt{3500}=\sqrt{100*35}=\sqrt{100}*\sqrt{35}=10\sqrt{35}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(50)-10\sqrt{35}}{2*25}=\frac{-50-10\sqrt{35}}{50}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(50)+10\sqrt{35}}{2*25}=\frac{-50+10\sqrt{35}}{50}
$