3/5x-7=6x+8

Solution for 3/5x-7=6x+8 equation:

3/5x-7=6x+8

We move all terms to the left:

3/5x-7-(6x+8)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We get rid of parentheses

3/5x-6x-8-7=0

We multiply all the terms by the denominator


-6x*5x-8*5x-7*5x+3=0

Wy multiply elements

-30x^2-40x-35x+3=0

We add all the numbers together, and all the variables

-30x^2-75x+3=0

a = -30; b = -75; c = +3;
Δ = b2-4ac
Δ = -752-4·(-30)·3
Δ = 5985
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:

$\sqrt{\Delta}=\sqrt{5985}=\sqrt{9*665}=\sqrt{9}*\sqrt{665}=3\sqrt{665}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-75)-3\sqrt{665}}{2*-30}=\frac{75-3\sqrt{665}}{-60}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-75)+3\sqrt{665}}{2*-30}=\frac{75+3\sqrt{665}}{-60}
$