10a(2a+6)=20

Solution for 10a(2a+6)=20 equation:

10a(2a+6)=20

We move all terms to the left:

10a(2a+6)-(20)=0

We multiply parentheses

20a^2+60a-20=0

a = 20; b = 60; c = -20;
Δ = b2-4ac
Δ = 602-4·20·(-20)
Δ = 5200
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{5200}=\sqrt{400*13}=\sqrt{400}*\sqrt{13}=20\sqrt{13}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(60)-20\sqrt{13}}{2*20}=\frac{-60-20\sqrt{13}}{40}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(60)+20\sqrt{13}}{2*20}=\frac{-60+20\sqrt{13}}{40}
$