X=4/5x+1

Solution for X=4/5x+1 equation:

X=4/5X+1

We move all terms to the left:

X-(4/5X+1)=0


Domain of the equation: 5X+1)!=0

X∈R


We get rid of parentheses

X-4/5X-1=0

We multiply all the terms by the denominator


X*5X-1*5X-4=0

Wy multiply elements

5X^2-5X-4=0

a = 5; b = -5; c = -4;
Δ = b2-4ac
Δ = -52-4·5·(-4)
Δ = 105
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{-(-5)-\sqrt{105}}{2*5}=\frac{5-\sqrt{105}}{10}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{105}}{2*5}=\frac{5+\sqrt{105}}{10}
$