15(2+x)3x=114

Solution for 15(2+x)3x=114 equation:

15(2+x)3x=114

We move all terms to the left:

15(2+x)3x-(114)=0

We add all the numbers together, and all the variables

15(x+2)3x-114=0

We multiply parentheses

45x^2+90x-114=0

a = 45; b = 90; c = -114;
Δ = b2-4ac
Δ = 902-4·45·(-114)
Δ = 28620
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:

$\sqrt{\Delta}=\sqrt{28620}=\sqrt{36*795}=\sqrt{36}*\sqrt{795}=6\sqrt{795}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(90)-6\sqrt{795}}{2*45}=\frac{-90-6\sqrt{795}}{90}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(90)+6\sqrt{795}}{2*45}=\frac{-90+6\sqrt{795}}{90}
$