(4/5)*x=120

Solution for (4/5)*x=120 equation:

(4/5)*x=120

We move all terms to the left:

(4/5)*x-(120)=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-120=0

We multiply parentheses

4x^2-120=0

a = 4; b = 0; c = -120;
Δ = b2-4ac
Δ = 02-4·4·(-120)
Δ = 1920
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:

$\sqrt{\Delta}=\sqrt{1920}=\sqrt{64*30}=\sqrt{64}*\sqrt{30}=8\sqrt{30}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{30}}{2*4}=\frac{0-8\sqrt{30}}{8}
=-\frac{8\sqrt{30}}{8}
=-\sqrt{30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{30}}{2*4}=\frac{0+8\sqrt{30}}{8}
=\frac{8\sqrt{30}}{8}
=\sqrt{30}
$