X/7x-4=5x-8

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

X/7X-4=5X-8

We move all terms to the left:

X/7X-4-(5X-8)=0


Domain of the equation: 7X!=0

X!=0/7

X!=0

X∈R


We get rid of parentheses

X/7X-5X+8-4=0

We multiply all the terms by the denominator


X-5X*7X+8*7X-4*7X=0

Wy multiply elements

-35X^2+X+56X-28X=0

We add all the numbers together, and all the variables

-35X^2+29X=0

a = -35; b = 29; c = 0;
Δ = b2-4ac
Δ = 292-4·(-35)·0
Δ = 841
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{841}=29$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(29)-29}{2*-35}=\frac{-58}{-70}
=29/35
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(29)+29}{2*-35}=\frac{0}{-70}
=0
$