3/5x+6=2x-8

Solution for 3/5x+6=2x-8 equation:

3/5x+6=2x-8

We move all terms to the left:

3/5x+6-(2x-8)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We get rid of parentheses

3/5x-2x+8+6=0

We multiply all the terms by the denominator


-2x*5x+8*5x+6*5x+3=0

Wy multiply elements

-10x^2+40x+30x+3=0

We add all the numbers together, and all the variables

-10x^2+70x+3=0

a = -10; b = 70; c = +3;
Δ = b2-4ac
Δ = 702-4·(-10)·3
Δ = 5020
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:

$\sqrt{\Delta}=\sqrt{5020}=\sqrt{4*1255}=\sqrt{4}*\sqrt{1255}=2\sqrt{1255}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(70)-2\sqrt{1255}}{2*-10}=\frac{-70-2\sqrt{1255}}{-20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(70)+2\sqrt{1255}}{2*-10}=\frac{-70+2\sqrt{1255}}{-20}
$