7x(x-8)=42

Solution for 7x(x-8)=42 equation:

7x(x-8)=42

We move all terms to the left:

7x(x-8)-(42)=0

We multiply parentheses

7x^2-56x-42=0

a = 7; b = -56; c = -42;
Δ = b2-4ac
Δ = -562-4·7·(-42)
Δ = 4312
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:

$\sqrt{\Delta}=\sqrt{4312}=\sqrt{196*22}=\sqrt{196}*\sqrt{22}=14\sqrt{22}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-56)-14\sqrt{22}}{2*7}=\frac{56-14\sqrt{22}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-56)+14\sqrt{22}}{2*7}=\frac{56+14\sqrt{22}}{14}
$