5x+3/2x-1=8

Solution for 5x+3/2x-1=8 equation:

5x+3/2x-1=8

We move all terms to the left:

5x+3/2x-1-(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

5x+3/2x-9=0

We multiply all the terms by the denominator


5x*2x-9*2x+3=0

Wy multiply elements

10x^2-18x+3=0

a = 10; b = -18; c = +3;
Δ = b2-4ac
Δ = -182-4·10·3
Δ = 204
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:

$\sqrt{\Delta}=\sqrt{204}=\sqrt{4*51}=\sqrt{4}*\sqrt{51}=2\sqrt{51}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-2\sqrt{51}}{2*10}=\frac{18-2\sqrt{51}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+2\sqrt{51}}{2*10}=\frac{18+2\sqrt{51}}{20}
$