X+3y=7X2-y2=39

Solution for X+3y=7X2-y2=39 equation:

X+3X=7X^2-X2=39

We move all terms to the left:

X+3X-(7X^2-X2)=0

We add all the numbers together, and all the variables

4X-(7X^2-X2)=0

We get rid of parentheses

-7X^2+4X+X2=0

We add all the numbers together, and all the variables

-6X^2+4X=0

a = -6; b = 4; c = 0;
Δ = b2-4ac
Δ = 42-4·(-6)·0
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4}{2*-6}=\frac{-8}{-12}
=2/3
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4}{2*-6}=\frac{0}{-12}
=0
$