X=4/5x+8

Solution for X=4/5x+8 equation:

X=4/5X+8

We move all terms to the left:

X-(4/5X+8)=0


Domain of the equation: 5X+8)!=0

X∈R


We get rid of parentheses

X-4/5X-8=0

We multiply all the terms by the denominator


X*5X-8*5X-4=0

Wy multiply elements

5X^2-40X-4=0

a = 5; b = -40; c = -4;
Δ = b2-4ac
Δ = -402-4·5·(-4)
Δ = 1680
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:

$\sqrt{\Delta}=\sqrt{1680}=\sqrt{16*105}=\sqrt{16}*\sqrt{105}=4\sqrt{105}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-4\sqrt{105}}{2*5}=\frac{40-4\sqrt{105}}{10}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+4\sqrt{105}}{2*5}=\frac{40+4\sqrt{105}}{10}
$