5x+16+4/5x-26=106

Solution for 5x+16+4/5x-26=106 equation:

5x+16+4/5x-26=106

We move all terms to the left:

5x+16+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-116=0

We multiply all the terms by the denominator


5x*5x-116*5x+4=0

Wy multiply elements

25x^2-580x+4=0

a = 25; b = -580; c = +4;
Δ = b2-4ac
Δ = -5802-4·25·4
Δ = 336000
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:

$\sqrt{\Delta}=\sqrt{336000}=\sqrt{1600*210}=\sqrt{1600}*\sqrt{210}=40\sqrt{210}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-580)-40\sqrt{210}}{2*25}=\frac{580-40\sqrt{210}}{50}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-580)+40\sqrt{210}}{2*25}=\frac{580+40\sqrt{210}}{50}
$