-x2+9x+7=21,x=2

Solution for -x2+9x+7=21,x=2 equation:

-x2+9x+7=21.x=2

We move all terms to the left:

-x2+9x+7-(21.x)=0

We add all the numbers together, and all the variables

-x2+9x-(+21.x)+7=0

We add all the numbers together, and all the variables

-1x^2+9x-(+21.x)+7=0

We get rid of parentheses

-1x^2+9x-21.x+7=0

We add all the numbers together, and all the variables

-1x^2-12x+7=0

a = -1; b = -12; c = +7;
Δ = b2-4ac
Δ = -122-4·(-1)·7
Δ = 172
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:

$\sqrt{\Delta}=\sqrt{172}=\sqrt{4*43}=\sqrt{4}*\sqrt{43}=2\sqrt{43}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-2\sqrt{43}}{2*-1}=\frac{12-2\sqrt{43}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+2\sqrt{43}}{2*-1}=\frac{12+2\sqrt{43}}{-2}
$