x(2x+15)=18

Solution for x(2x+15)=18 equation:

x(2x+15)=18

We move all terms to the left:

x(2x+15)-(18)=0

We multiply parentheses

2x^2+15x-18=0

a = 2; b = 15; c = -18;
Δ = b2-4ac
Δ = 152-4·2·(-18)
Δ = 369
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:

$\sqrt{\Delta}=\sqrt{369}=\sqrt{9*41}=\sqrt{9}*\sqrt{41}=3\sqrt{41}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-3\sqrt{41}}{2*2}=\frac{-15-3\sqrt{41}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+3\sqrt{41}}{2*2}=\frac{-15+3\sqrt{41}}{4}
$