12x^2-38x=-20

Solution for 12x^2-38x=-20 equation:

12x^2-38x=-20

We move all terms to the left:

12x^2-38x-(-20)=0

We add all the numbers together, and all the variables

12x^2-38x+20=0

a = 12; b = -38; c = +20;
Δ = b2-4ac
Δ = -382-4·12·20
Δ = 484
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{484}=22$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-38)-22}{2*12}=\frac{16}{24}
=2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-38)+22}{2*12}=\frac{60}{24}
=2+1/2
$