(x+9)2x+3=48

Solution for (x+9)2x+3=48 equation:

(x+9)2x+3=48

We move all terms to the left:

(x+9)2x+3-(48)=0

We add all the numbers together, and all the variables

(x+9)2x-45=0

We multiply parentheses

2x^2+18x-45=0

a = 2; b = 18; c = -45;
Δ = b2-4ac
Δ = 182-4·2·(-45)
Δ = 684
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:

$\sqrt{\Delta}=\sqrt{684}=\sqrt{36*19}=\sqrt{36}*\sqrt{19}=6\sqrt{19}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-6\sqrt{19}}{2*2}=\frac{-18-6\sqrt{19}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+6\sqrt{19}}{2*2}=\frac{-18+6\sqrt{19}}{4}
$