X^-2-49=(x+7)(-x+5)

Solution for X^-2-49=(x+7)(-x+5) equation:

X^-2-49=(X+7)(-X+5)

We move all terms to the left:

X^-2-49-((X+7)(-X+5))=0

We add all the numbers together, and all the variables

X^-((X+7)(-1X+5))-2-49=0

We add all the numbers together, and all the variables

X-((X+7)(-1X+5))-51=0

We multiply parentheses ..

-((-1X^2+5X-7X+35))+X-51=0


We calculate terms in parentheses: -((-1X^2+5X-7X+35)), so:

(-1X^2+5X-7X+35)

We get rid of parentheses

-1X^2+5X-7X+35

We add all the numbers together, and all the variables

-1X^2-2X+35

Back to the equation:

-(-1X^2-2X+35)


We get rid of parentheses

1X^2+2X+X-35-51=0

We add all the numbers together, and all the variables

X^2+3X-86=0

a = 1; b = 3; c = -86;
Δ = b2-4ac
Δ = 32-4·1·(-86)
Δ = 353
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{-(3)-\sqrt{353}}{2*1}=\frac{-3-\sqrt{353}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{353}}{2*1}=\frac{-3+\sqrt{353}}{2}
$