(3/5)x-3=3/8

Solution for (3/5)x-3=3/8 equation:

(3/5)x-3=3/8

We move all terms to the left:

(3/5)x-3-(3/8)=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

(+3/5)x-3-(+3/8)=0

We multiply parentheses

3x^2-3-(+3/8)=0

We get rid of parentheses

3x^2-3-3/8=0

We multiply all the terms by the denominator


3x^2*8-3-3*8=0

We add all the numbers together, and all the variables

3x^2*8-27=0

Wy multiply elements

24x^2-27=0

a = 24; b = 0; c = -27;
Δ = b2-4ac
Δ = 02-4·24·(-27)
Δ = 2592
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:

$\sqrt{\Delta}=\sqrt{2592}=\sqrt{1296*2}=\sqrt{1296}*\sqrt{2}=36\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-36\sqrt{2}}{2*24}=\frac{0-36\sqrt{2}}{48}
=-\frac{36\sqrt{2}}{48}
=-\frac{3\sqrt{2}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+36\sqrt{2}}{2*24}=\frac{0+36\sqrt{2}}{48}
=\frac{36\sqrt{2}}{48}
=\frac{3\sqrt{2}}{4}
$