2x(x+6)=188

Solution for 2x(x+6)=188 equation:

2x(x+6)=188

We move all terms to the left:

2x(x+6)-(188)=0

We multiply parentheses

2x^2+12x-188=0

a = 2; b = 12; c = -188;
Δ = b2-4ac
Δ = 122-4·2·(-188)
Δ = 1648
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:

$\sqrt{\Delta}=\sqrt{1648}=\sqrt{16*103}=\sqrt{16}*\sqrt{103}=4\sqrt{103}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-4\sqrt{103}}{2*2}=\frac{-12-4\sqrt{103}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+4\sqrt{103}}{2*2}=\frac{-12+4\sqrt{103}}{4}
$