x(2x+11)=156

Solution for x(2x+11)=156 equation:

x(2x+11)=156

We move all terms to the left:

x(2x+11)-(156)=0

We multiply parentheses

2x^2+11x-156=0

a = 2; b = 11; c = -156;
Δ = b2-4ac
Δ = 112-4·2·(-156)
Δ = 1369
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1369}=37$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-37}{2*2}=\frac{-48}{4}
=-12
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+37}{2*2}=\frac{26}{4}
=6+1/2
$