6x(x-5)=42

Solution for 6x(x-5)=42 equation:

6x(x-5)=42

We move all terms to the left:

6x(x-5)-(42)=0

We multiply parentheses

6x^2-30x-42=0

a = 6; b = -30; c = -42;
Δ = b2-4ac
Δ = -302-4·6·(-42)
Δ = 1908
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:

$\sqrt{\Delta}=\sqrt{1908}=\sqrt{36*53}=\sqrt{36}*\sqrt{53}=6\sqrt{53}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-6\sqrt{53}}{2*6}=\frac{30-6\sqrt{53}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+6\sqrt{53}}{2*6}=\frac{30+6\sqrt{53}}{12}
$