75x-5/5x+1=4

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Solution for 75x-5/5x+1=4 equation: 



75x-5/5x+1=4

We move all terms to the left:

75x-5/5x+1-(4)=0



Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



We add all the numbers together, and all the variables

75x-5/5x-3=0

We multiply all the terms by the denominator


75x*5x-3*5x-5=0

Wy multiply elements

375x^2-15x-5=0

a = 375; b = -15; c = -5;
Δ = b2-4ac
Δ = -152-4·375·(-5)
Δ = 7725
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:


$\sqrt{\Delta}=\sqrt{7725}=\sqrt{25*309}=\sqrt{25}*\sqrt{309}=5\sqrt{309}$


$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-5\sqrt{309}}{2*375}=\frac{15-5\sqrt{309}}{750}
$


$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+5\sqrt{309}}{2*375}=\frac{15+5\sqrt{309}}{750}
$

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