8x-5(x+3)=12x-7/3x+5-20

Solution for 8x-5(x+3)=12x-7/3x+5-20 equation:

8x-5(x+3)=12x-7/3x+5-20

We move all terms to the left:

8x-5(x+3)-(12x-7/3x+5-20)=0


Domain of the equation: 3x+5-20)!=0

We move all terms containing x to the left, all other terms to the right

3x-20)!=-5

x∈R


We add all the numbers together, and all the variables

8x-5(x+3)-(12x-7/3x-15)=0

We multiply parentheses

8x-5x-(12x-7/3x-15)-15=0

We get rid of parentheses

8x-5x-12x+7/3x+15-15=0

We multiply all the terms by the denominator


8x*3x-5x*3x-12x*3x+15*3x-15*3x+7=0

Wy multiply elements

24x^2-15x^2-36x^2+45x-45x+7=0

We add all the numbers together, and all the variables

-27x^2+7=0

a = -27; b = 0; c = +7;
Δ = b2-4ac
Δ = 02-4·(-27)·7
Δ = 756
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:

$\sqrt{\Delta}=\sqrt{756}=\sqrt{36*21}=\sqrt{36}*\sqrt{21}=6\sqrt{21}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{21}}{2*-27}=\frac{0-6\sqrt{21}}{-54}
=-\frac{6\sqrt{21}}{-54}
=-\frac{\sqrt{21}}{-9}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{21}}{2*-27}=\frac{0+6\sqrt{21}}{-54}
=\frac{6\sqrt{21}}{-54}
=\frac{\sqrt{21}}{-9}
$