5x^2+12=20x

Solution for 5x^2+12=20x equation:

5x^2+12=20x

We move all terms to the left:

5x^2+12-(20x)=0

a = 5; b = -20; c = +12;
Δ = b2-4ac
Δ = -202-4·5·12
Δ = 160
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:

$\sqrt{\Delta}=\sqrt{160}=\sqrt{16*10}=\sqrt{16}*\sqrt{10}=4\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-4\sqrt{10}}{2*5}=\frac{20-4\sqrt{10}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+4\sqrt{10}}{2*5}=\frac{20+4\sqrt{10}}{10}
$