5/7x-8=-8+3x

Solution for 5/7x-8=-8+3x equation:

5/7x-8=-8+3x

We move all terms to the left:

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


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

-21x^2+56x-56x+5=0

We add all the numbers together, and all the variables

-21x^2+5=0

a = -21; b = 0; c = +5;
Δ = b2-4ac
Δ = 02-4·(-21)·5
Δ = 420
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:

$\sqrt{\Delta}=\sqrt{420}=\sqrt{4*105}=\sqrt{4}*\sqrt{105}=2\sqrt{105}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{105}}{2*-21}=\frac{0-2\sqrt{105}}{-42}
=-\frac{2\sqrt{105}}{-42}
=-\frac{\sqrt{105}}{-21}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{105}}{2*-21}=\frac{0+2\sqrt{105}}{-42}
=\frac{2\sqrt{105}}{-42}
=\frac{\sqrt{105}}{-21}
$