-2x-8=-3/5x-5

Solution for -2x-8=-3/5x-5 equation:

-2x-8=-3/5x-5

We move all terms to the left:

-2x-8-(-3/5x-5)=0


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

x∈R


We get rid of parentheses

-2x+3/5x+5-8=0

We multiply all the terms by the denominator


-2x*5x+5*5x-8*5x+3=0

Wy multiply elements

-10x^2+25x-40x+3=0

We add all the numbers together, and all the variables

-10x^2-15x+3=0

a = -10; b = -15; c = +3;
Δ = b2-4ac
Δ = -152-4·(-10)·3
Δ = 345
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-\sqrt{345}}{2*-10}=\frac{15-\sqrt{345}}{-20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+\sqrt{345}}{2*-10}=\frac{15+\sqrt{345}}{-20}
$