(4/7)x+(5/14)x=39

Solution for (4/7)x+(5/14)x=39 equation:

(4/7)x+(5/14)x=39

We move all terms to the left:

(4/7)x+(5/14)x-(39)=0


Domain of the equation: 7)x!=0

x!=0/1

x!=0

x∈R



Domain of the equation: 14)x!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(+4/7)x+(+5/14)x-39=0

We multiply parentheses

4x^2+5x^2-39=0

We add all the numbers together, and all the variables

9x^2-39=0

a = 9; b = 0; c = -39;
Δ = b2-4ac
Δ = 02-4·9·(-39)
Δ = 1404
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:

$\sqrt{\Delta}=\sqrt{1404}=\sqrt{36*39}=\sqrt{36}*\sqrt{39}=6\sqrt{39}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{39}}{2*9}=\frac{0-6\sqrt{39}}{18}
=-\frac{6\sqrt{39}}{18}
=-\frac{\sqrt{39}}{3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{39}}{2*9}=\frac{0+6\sqrt{39}}{18}
=\frac{6\sqrt{39}}{18}
=\frac{\sqrt{39}}{3}
$