9/2x+3-2x=8

Solution for 9/2x+3-2x=8 equation:

9/2x+3-2x=8

We move all terms to the left:

9/2x+3-2x-(8)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

-2x+9/2x-5=0

We multiply all the terms by the denominator


-2x*2x-5*2x+9=0

Wy multiply elements

-4x^2-10x+9=0

a = -4; b = -10; c = +9;
Δ = b2-4ac
Δ = -102-4·(-4)·9
Δ = 244
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:

$\sqrt{\Delta}=\sqrt{244}=\sqrt{4*61}=\sqrt{4}*\sqrt{61}=2\sqrt{61}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{61}}{2*-4}=\frac{10-2\sqrt{61}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{61}}{2*-4}=\frac{10+2\sqrt{61}}{-8}
$