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

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

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

We move all terms to the left:

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


Domain of the equation: 2x-6)!=0

x∈R


We get rid of parentheses

5x-8/2x+6+4=0

We multiply all the terms by the denominator


5x*2x+6*2x+4*2x-8=0

Wy multiply elements

10x^2+12x+8x-8=0

We add all the numbers together, and all the variables

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}
$