(3/5)x-3=21/4

Solution for (3/5)x-3=21/4 equation:

(3/5)x-3=21/4

We move all terms to the left:

(3/5)x-3-(21/4)=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-(+21/4)=0

We multiply parentheses

3x^2-3-(+21/4)=0

We get rid of parentheses

3x^2-3-21/4=0

We multiply all the terms by the denominator


3x^2*4-21-3*4=0

We add all the numbers together, and all the variables

3x^2*4-33=0

Wy multiply elements

12x^2-33=0

a = 12; b = 0; c = -33;
Δ = b2-4ac
Δ = 02-4·12·(-33)
Δ = 1584
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:

$\sqrt{\Delta}=\sqrt{1584}=\sqrt{144*11}=\sqrt{144}*\sqrt{11}=12\sqrt{11}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{11}}{2*12}=\frac{0-12\sqrt{11}}{24}
=-\frac{12\sqrt{11}}{24}
=-\frac{\sqrt{11}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{11}}{2*12}=\frac{0+12\sqrt{11}}{24}
=\frac{12\sqrt{11}}{24}
=\frac{\sqrt{11}}{2}
$