12x^2-48x=-21

Solution for 12x^2-48x=-21 equation:

12x^2-48x=-21

We move all terms to the left:

12x^2-48x-(-21)=0

We add all the numbers together, and all the variables

12x^2-48x+21=0

a = 12; b = -48; c = +21;
Δ = b2-4ac
Δ = -482-4·12·21
Δ = 1296
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1296}=36$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-48)-36}{2*12}=\frac{12}{24}
=1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+36}{2*12}=\frac{84}{24}
=3+1/2
$