X=3/7x-13

Solution for X=3/7x-13 equation:

X=3/7X-13

We move all terms to the left:

X-(3/7X-13)=0


Domain of the equation: 7X-13)!=0

X∈R


We get rid of parentheses

X-3/7X+13=0

We multiply all the terms by the denominator


X*7X+13*7X-3=0

Wy multiply elements

7X^2+91X-3=0

a = 7; b = 91; c = -3;
Δ = b2-4ac
Δ = 912-4·7·(-3)
Δ = 8365
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{-(91)-\sqrt{8365}}{2*7}=\frac{-91-\sqrt{8365}}{14}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(91)+\sqrt{8365}}{2*7}=\frac{-91+\sqrt{8365}}{14}
$