2/5x-7=2x-2

Solution for 2/5x-7=2x-2 equation:

2/5x-7=2x-2

We move all terms to the left:

2/5x-7-(2x-2)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We get rid of parentheses

2/5x-2x+2-7=0

We multiply all the terms by the denominator


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

Wy multiply elements

-10x^2+10x-35x+2=0

We add all the numbers together, and all the variables

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

a = -10; b = -25; c = +2;
Δ = b2-4ac
Δ = -252-4·(-10)·2
Δ = 705
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{-(-25)-\sqrt{705}}{2*-10}=\frac{25-\sqrt{705}}{-20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-25)+\sqrt{705}}{2*-10}=\frac{25+\sqrt{705}}{-20}
$