X=6/5x+13

Solution for X=6/5x+13 equation:

X=6/5X+13

We move all terms to the left:

X-(6/5X+13)=0


Domain of the equation: 5X+13)!=0

X∈R


We get rid of parentheses

X-6/5X-13=0

We multiply all the terms by the denominator


X*5X-13*5X-6=0

Wy multiply elements

5X^2-65X-6=0

a = 5; b = -65; c = -6;
Δ = b2-4ac
Δ = -652-4·5·(-6)
Δ = 4345
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{-(-65)-\sqrt{4345}}{2*5}=\frac{65-\sqrt{4345}}{10}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-65)+\sqrt{4345}}{2*5}=\frac{65+\sqrt{4345}}{10}
$