(2/3)x-(3/4)=3

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

(2/3)x-(3/4)=3

We move all terms to the left:

(2/3)x-(3/4)-(3)=0


Domain of the equation: 3)x!=0

x!=0/1

x!=0

x∈R


determiningTheFunctionDomain
(2/3)x-3-(3/4)=0

We add all the numbers together, and all the variables

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

We multiply parentheses

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

We get rid of parentheses

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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

2x^2*4-15=0

Wy multiply elements

8x^2-15=0

a = 8; b = 0; c = -15;
Δ = b2-4ac
Δ = 02-4·8·(-15)
Δ = 480
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:

$\sqrt{\Delta}=\sqrt{480}=\sqrt{16*30}=\sqrt{16}*\sqrt{30}=4\sqrt{30}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{30}}{2*8}=\frac{0-4\sqrt{30}}{16}
=-\frac{4\sqrt{30}}{16}
=-\frac{\sqrt{30}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{30}}{2*8}=\frac{0+4\sqrt{30}}{16}
=\frac{4\sqrt{30}}{16}
=\frac{\sqrt{30}}{4}
$