(5/7)x+(1/3)x-27=17

Solution for (5/7)x+(1/3)x-27=17 equation:

(5/7)x+(1/3)x-27=17

We move all terms to the left:

(5/7)x+(1/3)x-27-(17)=0


Domain of the equation: 7)x!=0

x!=0/1

x!=0

x∈R



Domain of the equation: 3)x!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(+5/7)x+(+1/3)x-27-17=0

We add all the numbers together, and all the variables

(+5/7)x+(+1/3)x-44=0

We multiply parentheses

5x^2+x^2-44=0

We add all the numbers together, and all the variables

6x^2-44=0

a = 6; b = 0; c = -44;
Δ = b2-4ac
Δ = 02-4·6·(-44)
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*6}=\frac{0-4\sqrt{66}}{12}
=-\frac{4\sqrt{66}}{12}
=-\frac{\sqrt{66}}{3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{66}}{2*6}=\frac{0+4\sqrt{66}}{12}
=\frac{4\sqrt{66}}{12}
=\frac{\sqrt{66}}{3}
$