(5/4)x=120

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

(5/4)x=120

We move all terms to the left:

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


Domain of the equation: 4)x!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(+5/4)x-120=0

We multiply parentheses

5x^2-120=0

a = 5; b = 0; c = -120;
Δ = b2-4ac
Δ = 02-4·5·(-120)
Δ = 2400
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:

$\sqrt{\Delta}=\sqrt{2400}=\sqrt{400*6}=\sqrt{400}*\sqrt{6}=20\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-20\sqrt{6}}{2*5}=\frac{0-20\sqrt{6}}{10}
=-\frac{20\sqrt{6}}{10}
=-2\sqrt{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+20\sqrt{6}}{2*5}=\frac{0+20\sqrt{6}}{10}
=\frac{20\sqrt{6}}{10}
=2\sqrt{6}
$