(26/312)*x=1000

Solution for (26/312)*x=1000 equation:

(26/312)*x=1000

We move all terms to the left:

(26/312)*x-(1000)=0


Domain of the equation: 312)*x!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(+26/312)*x-1000=0

We multiply parentheses

26x^2-1000=0

a = 26; b = 0; c = -1000;
Δ = b2-4ac
Δ = 02-4·26·(-1000)
Δ = 104000
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:

$\sqrt{\Delta}=\sqrt{104000}=\sqrt{1600*65}=\sqrt{1600}*\sqrt{65}=40\sqrt{65}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-40\sqrt{65}}{2*26}=\frac{0-40\sqrt{65}}{52}
=-\frac{40\sqrt{65}}{52}
=-\frac{10\sqrt{65}}{13}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+40\sqrt{65}}{2*26}=\frac{0+40\sqrt{65}}{52}
=\frac{40\sqrt{65}}{52}
=\frac{10\sqrt{65}}{13}
$