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+96=0

We multiply all the terms by the denominator


5x*5x+96*5x+4=0

Wy multiply elements

25x^2+480x+4=0

a = 25; b = 480; c = +4;
Δ = b2-4ac
Δ = 4802-4·25·4
Δ = 230000
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:

$\sqrt{\Delta}=\sqrt{230000}=\sqrt{10000*23}=\sqrt{10000}*\sqrt{23}=100\sqrt{23}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(480)-100\sqrt{23}}{2*25}=\frac{-480-100\sqrt{23}}{50}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(480)+100\sqrt{23}}{2*25}=\frac{-480+100\sqrt{23}}{50}
$