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

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



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

We move all terms to the left:

5x+16+(4/5)x-26-(106)=0



Domain of the equation: 5)x!=0

x!=0/1

x!=0

x∈R



We add all the numbers together, and all the variables

5x+(+4/5)x+16-26-106=0

We add all the numbers together, and all the variables

5x+(+4/5)x-116=0

We multiply parentheses

4x^2+5x-116=0

a = 4; b = 5; c = -116;
Δ = b2-4ac
Δ = 52-4·4·(-116)
Δ = 1881
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:


$\sqrt{\Delta}=\sqrt{1881}=\sqrt{9*209}=\sqrt{9}*\sqrt{209}=3\sqrt{209}$


$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-3\sqrt{209}}{2*4}=\frac{-5-3\sqrt{209}}{8}
$


$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+3\sqrt{209}}{2*4}=\frac{-5+3\sqrt{209}}{8}
$

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