26=4x-3/5x-8

Solution for 26=4x-3/5x-8 equation:

26=4x-3/5x-8

We move all terms to the left:

26-(4x-3/5x-8)=0


Domain of the equation: 5x-8)!=0

x∈R


We get rid of parentheses

-4x+3/5x+8+26=0

We multiply all the terms by the denominator


-4x*5x+8*5x+26*5x+3=0

Wy multiply elements

-20x^2+40x+130x+3=0

We add all the numbers together, and all the variables

-20x^2+170x+3=0

a = -20; b = 170; c = +3;
Δ = b2-4ac
Δ = 1702-4·(-20)·3
Δ = 29140
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:

$\sqrt{\Delta}=\sqrt{29140}=\sqrt{4*7285}=\sqrt{4}*\sqrt{7285}=2\sqrt{7285}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(170)-2\sqrt{7285}}{2*-20}=\frac{-170-2\sqrt{7285}}{-40}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(170)+2\sqrt{7285}}{2*-20}=\frac{-170+2\sqrt{7285}}{-40}
$