x=-5/13x+3

Solution for x=-5/13x+3 equation:

x=-5/13x+3

We move all terms to the left:

x-(-5/13x+3)=0


Domain of the equation: 13x+3)!=0

x∈R


We get rid of parentheses

x+5/13x-3=0

We multiply all the terms by the denominator


x*13x-3*13x+5=0

Wy multiply elements

13x^2-39x+5=0

a = 13; b = -39; c = +5;
Δ = b2-4ac
Δ = -392-4·13·5
Δ = 1261
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{-(-39)-\sqrt{1261}}{2*13}=\frac{39-\sqrt{1261}}{26}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-39)+\sqrt{1261}}{2*13}=\frac{39+\sqrt{1261}}{26}
$