7x(x+2)=6

Solution for 7x(x+2)=6 equation:

7x(x+2)=6

We move all terms to the left:

7x(x+2)-(6)=0

We multiply parentheses

7x^2+14x-6=0

a = 7; b = 14; c = -6;
Δ = b2-4ac
Δ = 142-4·7·(-6)
Δ = 364
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:

$\sqrt{\Delta}=\sqrt{364}=\sqrt{4*91}=\sqrt{4}*\sqrt{91}=2\sqrt{91}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-2\sqrt{91}}{2*7}=\frac{-14-2\sqrt{91}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+2\sqrt{91}}{2*7}=\frac{-14+2\sqrt{91}}{14}
$