2x(x+9)-15=-3

Solution for 2x(x+9)-15=-3 equation:

2x(x+9)-15=-3

We move all terms to the left:

2x(x+9)-15-(-3)=0

We add all the numbers together, and all the variables

2x(x+9)-12=0

We multiply parentheses

2x^2+18x-12=0

a = 2; b = 18; c = -12;
Δ = b2-4ac
Δ = 182-4·2·(-12)
Δ = 420
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:

$\sqrt{\Delta}=\sqrt{420}=\sqrt{4*105}=\sqrt{4}*\sqrt{105}=2\sqrt{105}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-2\sqrt{105}}{2*2}=\frac{-18-2\sqrt{105}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+2\sqrt{105}}{2*2}=\frac{-18+2\sqrt{105}}{4}
$