x-45=5/8X

Solution for x-45=5/8X equation:

x-45=5/8x

We move all terms to the left:

x-45-(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)-45=0

We get rid of parentheses

x-5/8x-45=0

We multiply all the terms by the denominator


x*8x-45*8x-5=0

Wy multiply elements

8x^2-360x-5=0

a = 8; b = -360; c = -5;
Δ = b2-4ac
Δ = -3602-4·8·(-5)
Δ = 129760
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:

$\sqrt{\Delta}=\sqrt{129760}=\sqrt{16*8110}=\sqrt{16}*\sqrt{8110}=4\sqrt{8110}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-360)-4\sqrt{8110}}{2*8}=\frac{360-4\sqrt{8110}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-360)+4\sqrt{8110}}{2*8}=\frac{360+4\sqrt{8110}}{16}
$