6x^2+42x=36

Solution for 6x^2+42x=36 equation:

6x^2+42x=36

We move all terms to the left:

6x^2+42x-(36)=0

a = 6; b = 42; c = -36;
Δ = b2-4ac
Δ = 422-4·6·(-36)
Δ = 2628
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:

$\sqrt{\Delta}=\sqrt{2628}=\sqrt{36*73}=\sqrt{36}*\sqrt{73}=6\sqrt{73}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(42)-6\sqrt{73}}{2*6}=\frac{-42-6\sqrt{73}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(42)+6\sqrt{73}}{2*6}=\frac{-42+6\sqrt{73}}{12}
$