3x2+36x=42

Solution for 3x2+36x=42 equation:

3x^2+36x=42

We move all terms to the left:

3x^2+36x-(42)=0

a = 3; b = 36; c = -42;
Δ = b2-4ac
Δ = 362-4·3·(-42)
Δ = 1800
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:

$\sqrt{\Delta}=\sqrt{1800}=\sqrt{900*2}=\sqrt{900}*\sqrt{2}=30\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(36)-30\sqrt{2}}{2*3}=\frac{-36-30\sqrt{2}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+30\sqrt{2}}{2*3}=\frac{-36+30\sqrt{2}}{6}
$