-b2+10b+21=0

Solution for -b2+10b+21=0 equation:

-b2+10b+21=0

We add all the numbers together, and all the variables

-1b^2+10b+21=0

a = -1; b = 10; c = +21;
Δ = b2-4ac
Δ = 102-4·(-1)·21
Δ = 184
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{184}=\sqrt{4*46}=\sqrt{4}*\sqrt{46}=2\sqrt{46}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{46}}{2*-1}=\frac{-10-2\sqrt{46}}{-2}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{46}}{2*-1}=\frac{-10+2\sqrt{46}}{-2}
$