13/2x-5=5x-17

Solution for 13/2x-5=5x-17 equation:

13/2x-5=5x-17

We move all terms to the left:

13/2x-5-(5x-17)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We get rid of parentheses

13/2x-5x+17-5=0

We multiply all the terms by the denominator


-5x*2x+17*2x-5*2x+13=0

Wy multiply elements

-10x^2+34x-10x+13=0

We add all the numbers together, and all the variables

-10x^2+24x+13=0

a = -10; b = 24; c = +13;
Δ = b2-4ac
Δ = 242-4·(-10)·13
Δ = 1096
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1096}=\sqrt{4*274}=\sqrt{4}*\sqrt{274}=2\sqrt{274}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-2\sqrt{274}}{2*-10}=\frac{-24-2\sqrt{274}}{-20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+2\sqrt{274}}{2*-10}=\frac{-24+2\sqrt{274}}{-20}
$