3x^2+12x=75

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

3x^2+12x=75

We move all terms to the left:

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

a = 3; b = 12; c = -75;
Δ = b2-4ac
Δ = 122-4·3·(-75)
Δ = 1044
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:

$\sqrt{\Delta}=\sqrt{1044}=\sqrt{36*29}=\sqrt{36}*\sqrt{29}=6\sqrt{29}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-6\sqrt{29}}{2*3}=\frac{-12-6\sqrt{29}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+6\sqrt{29}}{2*3}=\frac{-12+6\sqrt{29}}{6}
$