5/7x-15=5x+30

Solution for 5/7x-15=5x+30 equation:

5/7x-15=5x+30

We move all terms to the left:

5/7x-15-(5x+30)=0


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R


We get rid of parentheses

5/7x-5x-30-15=0

We multiply all the terms by the denominator


-5x*7x-30*7x-15*7x+5=0

Wy multiply elements

-35x^2-210x-105x+5=0

We add all the numbers together, and all the variables

-35x^2-315x+5=0

a = -35; b = -315; c = +5;
Δ = b2-4ac
Δ = -3152-4·(-35)·5
Δ = 99925
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:

$\sqrt{\Delta}=\sqrt{99925}=\sqrt{25*3997}=\sqrt{25}*\sqrt{3997}=5\sqrt{3997}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-315)-5\sqrt{3997}}{2*-35}=\frac{315-5\sqrt{3997}}{-70}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-315)+5\sqrt{3997}}{2*-35}=\frac{315+5\sqrt{3997}}{-70}
$