X/5x+7=2x-2

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

X/5X+7=2X-2

We move all terms to the left:

X/5X+7-(2X-2)=0


Domain of the equation: 5X!=0

X!=0/5

X!=0

X∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

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

We add all the numbers together, and all the variables

-10X^2+46X=0

a = -10; b = 46; c = 0;
Δ = b2-4ac
Δ = 462-4·(-10)·0
Δ = 2116
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2116}=46$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(46)-46}{2*-10}=\frac{-92}{-20}
=4+3/5
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(46)+46}{2*-10}=\frac{0}{-20}
=0
$