5/2x-1=x+8

Solution for 5/2x-1=x+8 equation:

5/2x-1=x+8

We move all terms to the left:

5/2x-1-(x+8)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We get rid of parentheses

5/2x-x-8-1=0

We multiply all the terms by the denominator


-x*2x-8*2x-1*2x+5=0

Wy multiply elements

-2x^2-16x-2x+5=0

We add all the numbers together, and all the variables

-2x^2-18x+5=0

a = -2; b = -18; c = +5;
Δ = b2-4ac
Δ = -182-4·(-2)·5
Δ = 364
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:

$\sqrt{\Delta}=\sqrt{364}=\sqrt{4*91}=\sqrt{4}*\sqrt{91}=2\sqrt{91}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-2\sqrt{91}}{2*-2}=\frac{18-2\sqrt{91}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+2\sqrt{91}}{2*-2}=\frac{18+2\sqrt{91}}{-4}
$