X=6/7x-5

Solution for X=6/7x-5 equation:

X=6/7X-5

We move all terms to the left:

X-(6/7X-5)=0


Domain of the equation: 7X-5)!=0

X∈R


We get rid of parentheses

X-6/7X+5=0

We multiply all the terms by the denominator


X*7X+5*7X-6=0

Wy multiply elements

7X^2+35X-6=0

a = 7; b = 35; c = -6;
Δ = b2-4ac
Δ = 352-4·7·(-6)
Δ = 1393
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{1393}}{2*7}=\frac{-35-\sqrt{1393}}{14}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(35)+\sqrt{1393}}{2*7}=\frac{-35+\sqrt{1393}}{14}
$