5x-1=8/7x+4

Solution for 5x-1=8/7x+4 equation:

5x-1=8/7x+4

We move all terms to the left:

5x-1-(8/7x+4)=0


Domain of the equation: 7x+4)!=0

x∈R


We get rid of parentheses

5x-8/7x-4-1=0

We multiply all the terms by the denominator


5x*7x-4*7x-1*7x-8=0

Wy multiply elements

35x^2-28x-7x-8=0

We add all the numbers together, and all the variables

35x^2-35x-8=0

a = 35; b = -35; c = -8;
Δ = b2-4ac
Δ = -352-4·35·(-8)
Δ = 2345
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{-(-35)-\sqrt{2345}}{2*35}=\frac{35-\sqrt{2345}}{70}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-35)+\sqrt{2345}}{2*35}=\frac{35+\sqrt{2345}}{70}
$