3(6-4x)27x=10x-31

Solution for 3(6-4x)27x=10x-31 equation:

3(6-4x)27x=10x-31

We move all terms to the left:

3(6-4x)27x-(10x-31)=0

We add all the numbers together, and all the variables

3(-4x+6)27x-(10x-31)=0

We multiply parentheses

-324x^2+486x-(10x-31)=0

We get rid of parentheses

-324x^2+486x-10x+31=0

We add all the numbers together, and all the variables

-324x^2+476x+31=0

a = -324; b = 476; c = +31;
Δ = b2-4ac
Δ = 4762-4·(-324)·31
Δ = 266752
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:

$\sqrt{\Delta}=\sqrt{266752}=\sqrt{256*1042}=\sqrt{256}*\sqrt{1042}=16\sqrt{1042}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(476)-16\sqrt{1042}}{2*-324}=\frac{-476-16\sqrt{1042}}{-648}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(476)+16\sqrt{1042}}{2*-324}=\frac{-476+16\sqrt{1042}}{-648}
$