(26/52)*x=6

Solution for (26/52)*x=6 equation:

(26/52)*x=6

We move all terms to the left:

(26/52)*x-(6)=0


Domain of the equation: 52)*x!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(+26/52)*x-6=0

We multiply parentheses

26x^2-6=0

a = 26; b = 0; c = -6;
Δ = b2-4ac
Δ = 02-4·26·(-6)
Δ = 624
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:

$\sqrt{\Delta}=\sqrt{624}=\sqrt{16*39}=\sqrt{16}*\sqrt{39}=4\sqrt{39}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{39}}{2*26}=\frac{0-4\sqrt{39}}{52}
=-\frac{4\sqrt{39}}{52}
=-\frac{\sqrt{39}}{13}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{39}}{2*26}=\frac{0+4\sqrt{39}}{52}
=\frac{4\sqrt{39}}{52}
=\frac{\sqrt{39}}{13}
$