3x=-6(8-4x)+3/3

Solution for 3x=-6(8-4x)+3/3 equation:

3x=-6(8-4x)+3/3

We move all terms to the left:

3x-(-6(8-4x)+3/3)=0

We add all the numbers together, and all the variables

3x-(-6(-4x+8)+3/3)=0

We multiply all the terms by the denominator


3x*3)-(-6(-4x+8)+3=0

We multiply parentheses

3x*3)-(+24x-48+3=0

Wy multiply elements

9x^2+24x-48+3=0

We add all the numbers together, and all the variables

9x^2+24x-45=0

a = 9; b = 24; c = -45;
Δ = b2-4ac
Δ = 242-4·9·(-45)
Δ = 2196
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:

$\sqrt{\Delta}=\sqrt{2196}=\sqrt{36*61}=\sqrt{36}*\sqrt{61}=6\sqrt{61}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-6\sqrt{61}}{2*9}=\frac{-24-6\sqrt{61}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+6\sqrt{61}}{2*9}=\frac{-24+6\sqrt{61}}{18}
$