-x^2+7x+8=10

Solution for -x^2+7x+8=10 equation:

-x^2+7x+8=10

We move all terms to the left:

-x^2+7x+8-(10)=0

We add all the numbers together, and all the variables

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

a = -1; b = 7; c = -2;
Δ = b2-4ac
Δ = 72-4·(-1)·(-2)
Δ = 41
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{-(7)-\sqrt{41}}{2*-1}=\frac{-7-\sqrt{41}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{41}}{2*-1}=\frac{-7+\sqrt{41}}{-2}
$