X+7/5x+7/5x=76

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Solution for X+7/5x+7/5x=76 equation: 



X+7/5X+7/5X=76

We move all terms to the left:

X+7/5X+7/5X-(76)=0



Domain of the equation: 5X!=0

X!=0/5

X!=0

X∈R



We multiply all the terms by the denominator


X*5X-76*5X+7+7=0

We add all the numbers together, and all the variables

X*5X-76*5X+14=0

Wy multiply elements

5X^2-380X+14=0

a = 5; b = -380; c = +14;
Δ = b2-4ac
Δ = -3802-4·5·14
Δ = 144120
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:


$\sqrt{\Delta}=\sqrt{144120}=\sqrt{4*36030}=\sqrt{4}*\sqrt{36030}=2\sqrt{36030}$


$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-380)-2\sqrt{36030}}{2*5}=\frac{380-2\sqrt{36030}}{10}
$


$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-380)+2\sqrt{36030}}{2*5}=\frac{380+2\sqrt{36030}}{10}
$

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