5-5x=-5/2x+8x

Solution for 5-5x=-5/2x+8x equation:

5-5x=-5/2x+8x

We move all terms to the left:

5-5x-(-5/2x+8x)=0


Domain of the equation: 2x+8x)!=0

x∈R


We add all the numbers together, and all the variables

-5x-(+8x-5/2x)+5=0

We get rid of parentheses

-5x-8x+5/2x+5=0

We multiply all the terms by the denominator


-5x*2x-8x*2x+5*2x+5=0

Wy multiply elements

-10x^2-16x^2+10x+5=0

We add all the numbers together, and all the variables

-26x^2+10x+5=0

a = -26; b = 10; c = +5;
Δ = b2-4ac
Δ = 102-4·(-26)·5
Δ = 620
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:

$\sqrt{\Delta}=\sqrt{620}=\sqrt{4*155}=\sqrt{4}*\sqrt{155}=2\sqrt{155}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{155}}{2*-26}=\frac{-10-2\sqrt{155}}{-52}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{155}}{2*-26}=\frac{-10+2\sqrt{155}}{-52}
$