-2=4x-7/5x+1

Solution for -2=4x-7/5x+1 equation:

-2=4x-7/5x+1

We move all terms to the left:

-2-(4x-7/5x+1)=0


Domain of the equation: 5x+1)!=0

x∈R


We get rid of parentheses

-4x+7/5x-1-2=0

We multiply all the terms by the denominator


-4x*5x-1*5x-2*5x+7=0

Wy multiply elements

-20x^2-5x-10x+7=0

We add all the numbers together, and all the variables

-20x^2-15x+7=0

a = -20; b = -15; c = +7;
Δ = b2-4ac
Δ = -152-4·(-20)·7
Δ = 785
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{-(-15)-\sqrt{785}}{2*-20}=\frac{15-\sqrt{785}}{-40}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+\sqrt{785}}{2*-20}=\frac{15+\sqrt{785}}{-40}
$