2x(x+6)=7

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

2x(x+6)=7

We move all terms to the left:

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

We multiply parentheses

2x^2+12x-7=0

a = 2; b = 12; c = -7;
Δ = b2-4ac
Δ = 122-4·2·(-7)
Δ = 200
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:

$\sqrt{\Delta}=\sqrt{200}=\sqrt{100*2}=\sqrt{100}*\sqrt{2}=10\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-10\sqrt{2}}{2*2}=\frac{-12-10\sqrt{2}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+10\sqrt{2}}{2*2}=\frac{-12+10\sqrt{2}}{4}
$