(4/5)x=216

Solution for (4/5)x=216 equation:

(4/5)x=216

We move all terms to the left:

(4/5)x-(216)=0


Domain of the equation: 5)x!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(+4/5)x-216=0

We multiply parentheses

4x^2-216=0

a = 4; b = 0; c = -216;
Δ = b2-4ac
Δ = 02-4·4·(-216)
Δ = 3456
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:

$\sqrt{\Delta}=\sqrt{3456}=\sqrt{576*6}=\sqrt{576}*\sqrt{6}=24\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-24\sqrt{6}}{2*4}=\frac{0-24\sqrt{6}}{8}
=-\frac{24\sqrt{6}}{8}
=-3\sqrt{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+24\sqrt{6}}{2*4}=\frac{0+24\sqrt{6}}{8}
=\frac{24\sqrt{6}}{8}
=3\sqrt{6}
$