X=3/5x+8

Solution for X=3/5x+8 equation:

X=3/5X+8

We move all terms to the left:

X-(3/5X+8)=0


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

X∈R


We get rid of parentheses

X-3/5X-8=0

We multiply all the terms by the denominator


X*5X-8*5X-3=0

Wy multiply elements

5X^2-40X-3=0

a = 5; b = -40; c = -3;
Δ = b2-4ac
Δ = -402-4·5·(-3)
Δ = 1660
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:

$\sqrt{\Delta}=\sqrt{1660}=\sqrt{4*415}=\sqrt{4}*\sqrt{415}=2\sqrt{415}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-2\sqrt{415}}{2*5}=\frac{40-2\sqrt{415}}{10}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+2\sqrt{415}}{2*5}=\frac{40+2\sqrt{415}}{10}
$