3x^2-30x+75=12

Solution for 3x^2-30x+75=12 equation:

3x^2-30x+75=12

We move all terms to the left:

3x^2-30x+75-(12)=0

We add all the numbers together, and all the variables

3x^2-30x+63=0

a = 3; b = -30; c = +63;
Δ = b2-4ac
Δ = -302-4·3·63
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-12}{2*3}=\frac{18}{6}
=3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+12}{2*3}=\frac{42}{6}
=7
$