x=60+5/8x

Solution for x=60+5/8x equation:

x=60+5/8x

We move all terms to the left:

x-(60+5/8x)=0


Domain of the equation: 8x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

x-(5/8x+60)=0

We get rid of parentheses

x-5/8x-60=0

We multiply all the terms by the denominator


x*8x-60*8x-5=0

Wy multiply elements

8x^2-480x-5=0

a = 8; b = -480; c = -5;
Δ = b2-4ac
Δ = -4802-4·8·(-5)
Δ = 230560
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:

$\sqrt{\Delta}=\sqrt{230560}=\sqrt{16*14410}=\sqrt{16}*\sqrt{14410}=4\sqrt{14410}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-480)-4\sqrt{14410}}{2*8}=\frac{480-4\sqrt{14410}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-480)+4\sqrt{14410}}{2*8}=\frac{480+4\sqrt{14410}}{16}
$