7/5x-1=2x+8

Solution for 7/5x-1=2x+8 equation:

7/5x-1=2x+8

We move all terms to the left:

7/5x-1-(2x+8)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We get rid of parentheses

7/5x-2x-8-1=0

We multiply all the terms by the denominator


-2x*5x-8*5x-1*5x+7=0

Wy multiply elements

-10x^2-40x-5x+7=0

We add all the numbers together, and all the variables

-10x^2-45x+7=0

a = -10; b = -45; c = +7;
Δ = b2-4ac
Δ = -452-4·(-10)·7
Δ = 2305
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{-(-45)-\sqrt{2305}}{2*-10}=\frac{45-\sqrt{2305}}{-20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-45)+\sqrt{2305}}{2*-10}=\frac{45+\sqrt{2305}}{-20}
$