5/4x-17=x-8

Solution for 5/4x-17=x-8 equation:

5/4x-17=x-8

We move all terms to the left:

5/4x-17-(x-8)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We get rid of parentheses

5/4x-x+8-17=0

We multiply all the terms by the denominator


-x*4x+8*4x-17*4x+5=0

Wy multiply elements

-4x^2+32x-68x+5=0

We add all the numbers together, and all the variables

-4x^2-36x+5=0

a = -4; b = -36; c = +5;
Δ = b2-4ac
Δ = -362-4·(-4)·5
Δ = 1376
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:

$\sqrt{\Delta}=\sqrt{1376}=\sqrt{16*86}=\sqrt{16}*\sqrt{86}=4\sqrt{86}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-4\sqrt{86}}{2*-4}=\frac{36-4\sqrt{86}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+4\sqrt{86}}{2*-4}=\frac{36+4\sqrt{86}}{-8}
$