8x-5(x+3)=12x-1/2x+5-20

Solution for 8x-5(x+3)=12x-1/2x+5-20 equation:

8x-5(x+3)=12x-1/2x+5-20

We move all terms to the left:

8x-5(x+3)-(12x-1/2x+5-20)=0


Domain of the equation: 2x+5-20)!=0

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

2x-20)!=-5

x∈R


We add all the numbers together, and all the variables

8x-5(x+3)-(12x-1/2x-15)=0

We multiply parentheses

8x-5x-(12x-1/2x-15)-15=0

We get rid of parentheses

8x-5x-12x+1/2x+15-15=0

We multiply all the terms by the denominator


8x*2x-5x*2x-12x*2x+15*2x-15*2x+1=0

Wy multiply elements

16x^2-10x^2-24x^2+30x-30x+1=0

We add all the numbers together, and all the variables

-18x^2+1=0

a = -18; b = 0; c = +1;
Δ = b2-4ac
Δ = 02-4·(-18)·1
Δ = 72
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:

$\sqrt{\Delta}=\sqrt{72}=\sqrt{36*2}=\sqrt{36}*\sqrt{2}=6\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{2}}{2*-18}=\frac{0-6\sqrt{2}}{-36}
=-\frac{6\sqrt{2}}{-36}
=-\frac{\sqrt{2}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{2}}{2*-18}=\frac{0+6\sqrt{2}}{-36}
=\frac{6\sqrt{2}}{-36}
=\frac{\sqrt{2}}{-6}
$