2x(x+6)=153

Solution for 2x(x+6)=153 equation:

2x(x+6)=153

We move all terms to the left:

2x(x+6)-(153)=0

We multiply parentheses

2x^2+12x-153=0

a = 2; b = 12; c = -153;
Δ = b2-4ac
Δ = 122-4·2·(-153)
Δ = 1368
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:

$\sqrt{\Delta}=\sqrt{1368}=\sqrt{36*38}=\sqrt{36}*\sqrt{38}=6\sqrt{38}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-6\sqrt{38}}{2*2}=\frac{-12-6\sqrt{38}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+6\sqrt{38}}{2*2}=\frac{-12+6\sqrt{38}}{4}
$