3(-4x+5)6x=15

Solution for 3(-4x+5)6x=15 equation:

3(-4x+5)6x=15

We move all terms to the left:

3(-4x+5)6x-(15)=0

We multiply parentheses

-72x^2+90x-15=0

a = -72; b = 90; c = -15;
Δ = b2-4ac
Δ = 902-4·(-72)·(-15)
Δ = 3780
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:

$\sqrt{\Delta}=\sqrt{3780}=\sqrt{36*105}=\sqrt{36}*\sqrt{105}=6\sqrt{105}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(90)-6\sqrt{105}}{2*-72}=\frac{-90-6\sqrt{105}}{-144}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(90)+6\sqrt{105}}{2*-72}=\frac{-90+6\sqrt{105}}{-144}
$