3x(4+x)6+15=48

Solution for 3x(4+x)6+15=48 equation:

3x(4+x)6+15=48

We move all terms to the left:

3x(4+x)6+15-(48)=0

We add all the numbers together, and all the variables

3x(x+4)6+15-48=0

We add all the numbers together, and all the variables

3x(x+4)6-33=0

We multiply parentheses

18x^2+72x-33=0

a = 18; b = 72; c = -33;
Δ = b2-4ac
Δ = 722-4·18·(-33)
Δ = 7560
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:

$\sqrt{\Delta}=\sqrt{7560}=\sqrt{36*210}=\sqrt{36}*\sqrt{210}=6\sqrt{210}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(72)-6\sqrt{210}}{2*18}=\frac{-72-6\sqrt{210}}{36}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(72)+6\sqrt{210}}{2*18}=\frac{-72+6\sqrt{210}}{36}
$