X^2+(y-8)=41^1(2-7)^2

Solution for X^2+(y-8)=41^1(2-7)^2 equation:

X^2+(X-8)=41^1(2-7)^2

We move all terms to the left:

X^2+(X-8)-(41^1(2-7)^2)=0

We add all the numbers together, and all the variables

X^2+(X-8)-(41^1(-5)^2)=0

We add all the numbers together, and all the variables

X^2+(X-8)-1025=0

We get rid of parentheses

X^2+X-8-1025=0

We add all the numbers together, and all the variables

X^2+X-1033=0

a = 1; b = 1; c = -1033;
Δ = b2-4ac
Δ = 12-4·1·(-1033)
Δ = 4133
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-\sqrt{4133}}{2*1}=\frac{-1-\sqrt{4133}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{4133}}{2*1}=\frac{-1+\sqrt{4133}}{2}
$