4(3a+5)a=5

Solution for 4(3a+5)a=5 equation:

4(3a+5)a=5

We move all terms to the left:

4(3a+5)a-(5)=0

We multiply parentheses

12a^2+20a-5=0

a = 12; b = 20; c = -5;
Δ = b2-4ac
Δ = 202-4·12·(-5)
Δ = 640
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:

$\sqrt{\Delta}=\sqrt{640}=\sqrt{64*10}=\sqrt{64}*\sqrt{10}=8\sqrt{10}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-8\sqrt{10}}{2*12}=\frac{-20-8\sqrt{10}}{24}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+8\sqrt{10}}{2*12}=\frac{-20+8\sqrt{10}}{24}
$