4a^2-20a+12=0

Solution for 4a^2-20a+12=0 equation:

4a^2-20a+12=0

a = 4; b = -20; c = +12;
Δ = b2-4ac
Δ = -202-4·4·12
Δ = 208
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:

$\sqrt{\Delta}=\sqrt{208}=\sqrt{16*13}=\sqrt{16}*\sqrt{13}=4\sqrt{13}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-4\sqrt{13}}{2*4}=\frac{20-4\sqrt{13}}{8}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+4\sqrt{13}}{2*4}=\frac{20+4\sqrt{13}}{8}
$