X-35=4/5x

Solution for X-35=4/5x equation:

X-35=4/5X

We move all terms to the left:

X-35-(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)-35=0

We get rid of parentheses

X-4/5X-35=0

We multiply all the terms by the denominator


X*5X-35*5X-4=0

Wy multiply elements

5X^2-175X-4=0

a = 5; b = -175; c = -4;
Δ = b2-4ac
Δ = -1752-4·5·(-4)
Δ = 30705
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-175)-\sqrt{30705}}{2*5}=\frac{175-\sqrt{30705}}{10}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-175)+\sqrt{30705}}{2*5}=\frac{175+\sqrt{30705}}{10}
$