(5/8)x=72

Solution for (5/8)x=72 equation:

(5/8)x=72

We move all terms to the left:

(5/8)x-(72)=0


Domain of the equation: 8)x!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(+5/8)x-72=0

We multiply parentheses

5x^2-72=0

a = 5; b = 0; c = -72;
Δ = b2-4ac
Δ = 02-4·5·(-72)
Δ = 1440
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:

$\sqrt{\Delta}=\sqrt{1440}=\sqrt{144*10}=\sqrt{144}*\sqrt{10}=12\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{10}}{2*5}=\frac{0-12\sqrt{10}}{10}
=-\frac{12\sqrt{10}}{10}
=-\frac{6\sqrt{10}}{5}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{10}}{2*5}=\frac{0+12\sqrt{10}}{10}
=\frac{12\sqrt{10}}{10}
=\frac{6\sqrt{10}}{5}
$