x(5/6)-(1/2)=7

Solution for x(5/6)-(1/2)=7 equation:

x(5/6)-(1/2)=7

We move all terms to the left:

x(5/6)-(1/2)-(7)=0

determiningTheFunctionDomain
x(5/6)-7-(1/2)=0

We add all the numbers together, and all the variables

x(+5/6)-7-(+1/2)=0

We multiply parentheses

5x^2-7-(+1/2)=0

We get rid of parentheses

5x^2-7-1/2=0

We multiply all the terms by the denominator


5x^2*2-1-7*2=0

We add all the numbers together, and all the variables

5x^2*2-15=0

Wy multiply elements

10x^2-15=0

a = 10; b = 0; c = -15;
Δ = b2-4ac
Δ = 02-4·10·(-15)
Δ = 600
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:

$\sqrt{\Delta}=\sqrt{600}=\sqrt{100*6}=\sqrt{100}*\sqrt{6}=10\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-10\sqrt{6}}{2*10}=\frac{0-10\sqrt{6}}{20}
=-\frac{10\sqrt{6}}{20}
=-\frac{\sqrt{6}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+10\sqrt{6}}{2*10}=\frac{0+10\sqrt{6}}{20}
=\frac{10\sqrt{6}}{20}
=\frac{\sqrt{6}}{2}
$