X=4a-5/2a+1

Solution for X=4a-5/2a+1 equation:

X=4X-5/2X+1

We move all terms to the left:

X-(4X-5/2X+1)=0


Domain of the equation: 2X+1)!=0

X∈R


We get rid of parentheses

X-4X+5/2X-1=0

We multiply all the terms by the denominator


X*2X-4X*2X-1*2X+5=0

Wy multiply elements

2X^2-8X^2-2X+5=0

We add all the numbers together, and all the variables

-6X^2-2X+5=0

a = -6; b = -2; c = +5;
Δ = b2-4ac
Δ = -22-4·(-6)·5
Δ = 124
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:

$\sqrt{\Delta}=\sqrt{124}=\sqrt{4*31}=\sqrt{4}*\sqrt{31}=2\sqrt{31}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{31}}{2*-6}=\frac{2-2\sqrt{31}}{-12}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{31}}{2*-6}=\frac{2+2\sqrt{31}}{-12}
$