X=65y-10.5y^2

Solution for X=65y-10.5y^2 equation:

X=65X-10.5X^2

We move all terms to the left:

X-(65X-10.5X^2)=0

We get rid of parentheses

10.5X^2-65X+X=0

We add all the numbers together, and all the variables

10.5X^2-64X=0

a = 10.5; b = -64; c = 0;
Δ = b2-4ac
Δ = -642-4·10.5·0
Δ = 4096
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4096}=64$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-64)-64}{2*10.5}=\frac{0}{21}
=0
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-64)+64}{2*10.5}=\frac{128}{21}
=6+2/21
$