8x-5(x+3)=12x-7/4x+5-20

Solution for 8x-5(x+3)=12x-7/4x+5-20 equation:

8x-5(x+3)=12x-7/4x+5-20

We move all terms to the left:

8x-5(x+3)-(12x-7/4x+5-20)=0


Domain of the equation: 4x+5-20)!=0

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

4x-20)!=-5

x∈R


We add all the numbers together, and all the variables

8x-5(x+3)-(12x-7/4x-15)=0

We multiply parentheses

8x-5x-(12x-7/4x-15)-15=0

We get rid of parentheses

8x-5x-12x+7/4x+15-15=0

We multiply all the terms by the denominator


8x*4x-5x*4x-12x*4x+15*4x-15*4x+7=0

Wy multiply elements

32x^2-20x^2-48x^2+60x-60x+7=0

We add all the numbers together, and all the variables

-36x^2+7=0

a = -36; b = 0; c = +7;
Δ = b2-4ac
Δ = 02-4·(-36)·7
Δ = 1008
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:

$\sqrt{\Delta}=\sqrt{1008}=\sqrt{144*7}=\sqrt{144}*\sqrt{7}=12\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{7}}{2*-36}=\frac{0-12\sqrt{7}}{-72}
=-\frac{12\sqrt{7}}{-72}
=-\frac{\sqrt{7}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{7}}{2*-36}=\frac{0+12\sqrt{7}}{-72}
=\frac{12\sqrt{7}}{-72}
=\frac{\sqrt{7}}{-6}
$