x=5/2x-1-3

Solution for x=5/2x-1-3 equation:

x=5/2x-1-3

We move all terms to the left:

x-(5/2x-1-3)=0


Domain of the equation: 2x-1-3)!=0

We move all terms containing x to the left, all other terms to the right

2x-3)!=1

x∈R


We add all the numbers together, and all the variables

x-(5/2x-4)=0

We get rid of parentheses

x-5/2x+4=0

We multiply all the terms by the denominator


x*2x+4*2x-5=0

Wy multiply elements

2x^2+8x-5=0

a = 2; b = 8; c = -5;
Δ = b2-4ac
Δ = 82-4·2·(-5)
Δ = 104
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:

$\sqrt{\Delta}=\sqrt{104}=\sqrt{4*26}=\sqrt{4}*\sqrt{26}=2\sqrt{26}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-2\sqrt{26}}{2*2}=\frac{-8-2\sqrt{26}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+2\sqrt{26}}{2*2}=\frac{-8+2\sqrt{26}}{4}
$