X-4/5x=25

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Solution for X-4/5x=25 equation:



X-4/5X=25
We move all terms to the left:
X-4/5X-(25)=0
Domain of the equation: 5X!=0
X!=0/5
X!=0
X∈R
We multiply all the terms by the denominator
X*5X-25*5X-4=0
Wy multiply elements
5X^2-125X-4=0
a = 5; b = -125; c = -4;
Δ = b2-4ac
Δ = -1252-4·5·(-4)
Δ = 15705
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:
$\sqrt{\Delta}=\sqrt{15705}=\sqrt{9*1745}=\sqrt{9}*\sqrt{1745}=3\sqrt{1745}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-125)-3\sqrt{1745}}{2*5}=\frac{125-3\sqrt{1745}}{10} $
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-125)+3\sqrt{1745}}{2*5}=\frac{125+3\sqrt{1745}}{10} $

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