X(5/8x)=360

Solution for X(5/8x)=360 equation:

X(5/8X)=360

We move all terms to the left:

X(5/8X)-(360)=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)-360=0

We multiply parentheses

5X^2-360=0

a = 5; b = 0; c = -360;
Δ = b2-4ac
Δ = 02-4·5·(-360)
Δ = 7200
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:

$\sqrt{\Delta}=\sqrt{7200}=\sqrt{3600*2}=\sqrt{3600}*\sqrt{2}=60\sqrt{2}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-60\sqrt{2}}{2*5}=\frac{0-60\sqrt{2}}{10}
=-\frac{60\sqrt{2}}{10}
=-6\sqrt{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+60\sqrt{2}}{2*5}=\frac{0+60\sqrt{2}}{10}
=\frac{60\sqrt{2}}{10}
=6\sqrt{2}
$