X-25=4/5x

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

X-25=4/5X

We move all terms to the left:

X-25-(4/5X)=0


Domain of the equation: 5X)!=0

X!=0/1

X!=0

X∈R


We add all the numbers together, and all the variables

X-(+4/5X)-25=0

We get rid of parentheses

X-4/5X-25=0

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}
$