(4/5)x-(1/3)=7

Solution for (4/5)x-(1/3)=7 equation:

(4/5)x-(1/3)=7

We move all terms to the left:

(4/5)x-(1/3)-(7)=0


Domain of the equation: 5)x!=0

x!=0/1

x!=0

x∈R


determiningTheFunctionDomain
(4/5)x-7-(1/3)=0

We add all the numbers together, and all the variables

(+4/5)x-7-(+1/3)=0

We multiply parentheses

4x^2-7-(+1/3)=0

We get rid of parentheses

4x^2-7-1/3=0

We multiply all the terms by the denominator


4x^2*3-1-7*3=0

We add all the numbers together, and all the variables

4x^2*3-22=0

Wy multiply elements

12x^2-22=0

a = 12; b = 0; c = -22;
Δ = b2-4ac
Δ = 02-4·12·(-22)
Δ = 1056
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:

$\sqrt{\Delta}=\sqrt{1056}=\sqrt{16*66}=\sqrt{16}*\sqrt{66}=4\sqrt{66}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{66}}{2*12}=\frac{0-4\sqrt{66}}{24}
=-\frac{4\sqrt{66}}{24}
=-\frac{\sqrt{66}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{66}}{2*12}=\frac{0+4\sqrt{66}}{24}
=\frac{4\sqrt{66}}{24}
=\frac{\sqrt{66}}{6}
$