10=-4.5x^2+5.6x+8.7

Solution for 10=-4.5x^2+5.6x+8.7 equation:

10=-4.5x^2+5.6x+8.7

We move all terms to the left:

10-(-4.5x^2+5.6x+8.7)=0

We get rid of parentheses

4.5x^2-5.6x-8.7+10=0

We add all the numbers together, and all the variables

4.5x^2-5.6x+1.3=0

a = 4.5; b = -5.6; c = +1.3;
Δ = b2-4ac
Δ = -5.62-4·4.5·1.3
Δ = 7.96
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{-(-5.6)-\sqrt{7.96}}{2*4.5}=\frac{5.6-\sqrt{7.96}}{9}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5.6)+\sqrt{7.96}}{2*4.5}=\frac{5.6+\sqrt{7.96}}{9}
$