3x^2-42x=39

Solution for 3x^2-42x=39 equation:

3x^2-42x=39

We move all terms to the left:

3x^2-42x-(39)=0

a = 3; b = -42; c = -39;
Δ = b2-4ac
Δ = -422-4·3·(-39)
Δ = 2232
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:

$\sqrt{\Delta}=\sqrt{2232}=\sqrt{36*62}=\sqrt{36}*\sqrt{62}=6\sqrt{62}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-42)-6\sqrt{62}}{2*3}=\frac{42-6\sqrt{62}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-42)+6\sqrt{62}}{2*3}=\frac{42+6\sqrt{62}}{6}
$