3x^2+30x-75=-27

Solution for 3x^2+30x-75=-27 equation:

3x^2+30x-75=-27

We move all terms to the left:

3x^2+30x-75-(-27)=0

We add all the numbers together, and all the variables

3x^2+30x-48=0

a = 3; b = 30; c = -48;
Δ = b2-4ac
Δ = 302-4·3·(-48)
Δ = 1476
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:

$\sqrt{\Delta}=\sqrt{1476}=\sqrt{36*41}=\sqrt{36}*\sqrt{41}=6\sqrt{41}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-6\sqrt{41}}{2*3}=\frac{-30-6\sqrt{41}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+6\sqrt{41}}{2*3}=\frac{-30+6\sqrt{41}}{6}
$