-5x+8/2x-6=4

Solution for -5x+8/2x-6=4 equation:

-5x+8/2x-6=4

We move all terms to the left:

-5x+8/2x-6-(4)=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-10=0

We multiply all the terms by the denominator


-5x*2x-10*2x+8=0

Wy multiply elements

-10x^2-20x+8=0

a = -10; b = -20; c = +8;
Δ = b2-4ac
Δ = -202-4·(-10)·8
Δ = 720
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:

$\sqrt{\Delta}=\sqrt{720}=\sqrt{144*5}=\sqrt{144}*\sqrt{5}=12\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-12\sqrt{5}}{2*-10}=\frac{20-12\sqrt{5}}{-20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+12\sqrt{5}}{2*-10}=\frac{20+12\sqrt{5}}{-20}
$