3x=-5(6-4x)+2/4

Solution for 3x=-5(6-4x)+2/4 equation:

3x=-5(6-4x)+2/4

We move all terms to the left:

3x-(-5(6-4x)+2/4)=0

We add all the numbers together, and all the variables

3x-(-5(-4x+6)+2/4)=0

We multiply all the terms by the denominator


3x*4)-(-5(-4x+6)+2=0

We multiply parentheses

3x*4)-(+20x-30+2=0

Wy multiply elements

12x^2+20x-30+2=0

We add all the numbers together, and all the variables

12x^2+20x-28=0

a = 12; b = 20; c = -28;
Δ = b2-4ac
Δ = 202-4·12·(-28)
Δ = 1744
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:

$\sqrt{\Delta}=\sqrt{1744}=\sqrt{16*109}=\sqrt{16}*\sqrt{109}=4\sqrt{109}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-4\sqrt{109}}{2*12}=\frac{-20-4\sqrt{109}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+4\sqrt{109}}{2*12}=\frac{-20+4\sqrt{109}}{24}
$