10(2c+5)c=5

Solution for 10(2c+5)c=5 equation:

10(2c+5)c=5

We move all terms to the left:

10(2c+5)c-(5)=0

We multiply parentheses

20c^2+50c-5=0

a = 20; b = 50; c = -5;
Δ = b2-4ac
Δ = 502-4·20·(-5)
Δ = 2900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{2900}=\sqrt{100*29}=\sqrt{100}*\sqrt{29}=10\sqrt{29}$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(50)-10\sqrt{29}}{2*20}=\frac{-50-10\sqrt{29}}{40}
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(50)+10\sqrt{29}}{2*20}=\frac{-50+10\sqrt{29}}{40}
$