6(2x+1)3x=15

Solution for 6(2x+1)3x=15 equation:

6(2x+1)3x=15

We move all terms to the left:

6(2x+1)3x-(15)=0

We multiply parentheses

36x^2+18x-15=0

a = 36; b = 18; c = -15;
Δ = b2-4ac
Δ = 182-4·36·(-15)
Δ = 2484
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:

$\sqrt{\Delta}=\sqrt{2484}=\sqrt{36*69}=\sqrt{36}*\sqrt{69}=6\sqrt{69}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-6\sqrt{69}}{2*36}=\frac{-18-6\sqrt{69}}{72}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+6\sqrt{69}}{2*36}=\frac{-18+6\sqrt{69}}{72}
$