7x(x+2)=42

Solution for 7x(x+2)=42 equation:

7x(x+2)=42

We move all terms to the left:

7x(x+2)-(42)=0

We multiply parentheses

7x^2+14x-42=0

a = 7; b = 14; c = -42;
Δ = b2-4ac
Δ = 142-4·7·(-42)
Δ = 1372
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:

$\sqrt{\Delta}=\sqrt{1372}=\sqrt{196*7}=\sqrt{196}*\sqrt{7}=14\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-14\sqrt{7}}{2*7}=\frac{-14-14\sqrt{7}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+14\sqrt{7}}{2*7}=\frac{-14+14\sqrt{7}}{14}
$