(X/5)-4=(3/2)x-1

Solution for (X/5)-4=(3/2)x-1 equation:

(X/5)-4=(3/2)X-1

We move all terms to the left:

(X/5)-4-((3/2)X-1)=0


Domain of the equation: 2)X-1)!=0

X!=0/1

X!=0

X∈R


We add all the numbers together, and all the variables

(+X/5)-((+3/2)X-1)-4=0

We get rid of parentheses

X/5-((+3/2)X-1)-4=0

We calculate fractions


2X^2/10X+()/10X-4=0

We multiply all the terms by the denominator


2X^2-4*10X+()=0

We add all the numbers together, and all the variables

2X^2-4*10X=0

Wy multiply elements

2X^2-40X=0

a = 2; b = -40; c = 0;
Δ = b2-4ac
Δ = -402-4·2·0
Δ = 1600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1600}=40$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-40}{2*2}=\frac{0}{4}
=0
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+40}{2*2}=\frac{80}{4}
=20
$