5x+6+4/5x-26=106

Solution for 5x+6+4/5x-26=106 equation:

5x+6+4/5x-26=106

We move all terms to the left:

5x+6+4/5x-26-(106)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We add all the numbers together, and all the variables

5x+4/5x-126=0

We multiply all the terms by the denominator


5x*5x-126*5x+4=0

Wy multiply elements

25x^2-630x+4=0

a = 25; b = -630; c = +4;
Δ = b2-4ac
Δ = -6302-4·25·4
Δ = 396500
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:

$\sqrt{\Delta}=\sqrt{396500}=\sqrt{100*3965}=\sqrt{100}*\sqrt{3965}=10\sqrt{3965}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-630)-10\sqrt{3965}}{2*25}=\frac{630-10\sqrt{3965}}{50}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-630)+10\sqrt{3965}}{2*25}=\frac{630+10\sqrt{3965}}{50}
$