27x^2=-48x+12

Solution for 27x^2=-48x+12 equation:

27x^2=-48x+12

We move all terms to the left:

27x^2-(-48x+12)=0

We get rid of parentheses

27x^2+48x-12=0

a = 27; b = 48; c = -12;
Δ = b2-4ac
Δ = 482-4·27·(-12)
Δ = 3600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3600}=60$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(48)-60}{2*27}=\frac{-108}{54}
=-2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(48)+60}{2*27}=\frac{12}{54}
=2/9
$