X+2/13y=75

Solution for X+2/13y=75 equation:

X+2/13X=75

We move all terms to the left:

X+2/13X-(75)=0


Domain of the equation: 13X!=0

X!=0/13

X!=0

X∈R


We multiply all the terms by the denominator


X*13X-75*13X+2=0

Wy multiply elements

13X^2-975X+2=0

a = 13; b = -975; c = +2;
Δ = b2-4ac
Δ = -9752-4·13·2
Δ = 950521
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:

$\sqrt{\Delta}=\sqrt{950521}=\sqrt{289*3289}=\sqrt{289}*\sqrt{3289}=17\sqrt{3289}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-975)-17\sqrt{3289}}{2*13}=\frac{975-17\sqrt{3289}}{26}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-975)+17\sqrt{3289}}{2*13}=\frac{975+17\sqrt{3289}}{26}
$