5x-8/2x=7+4x-9

Solution for 5x-8/2x=7+4x-9 equation:

5x-8/2x=7+4x-9

We move all terms to the left:

5x-8/2x-(7+4x-9)=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-8/2x-(4x-2)=0

We get rid of parentheses

5x-8/2x-4x+2=0

We multiply all the terms by the denominator


5x*2x-4x*2x+2*2x-8=0

Wy multiply elements

10x^2-8x^2+4x-8=0

We add all the numbers together, and all the variables

2x^2+4x-8=0

a = 2; b = 4; c = -8;
Δ = b2-4ac
Δ = 42-4·2·(-8)
Δ = 80
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:

$\sqrt{\Delta}=\sqrt{80}=\sqrt{16*5}=\sqrt{16}*\sqrt{5}=4\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4\sqrt{5}}{2*2}=\frac{-4-4\sqrt{5}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4\sqrt{5}}{2*2}=\frac{-4+4\sqrt{5}}{4}
$