10=-16x^2+22x+3

Solution for 10=-16x^2+22x+3 equation:

10=-16x^2+22x+3

We move all terms to the left:

10-(-16x^2+22x+3)=0

We get rid of parentheses

16x^2-22x-3+10=0

We add all the numbers together, and all the variables

16x^2-22x+7=0

a = 16; b = -22; c = +7;
Δ = b2-4ac
Δ = -222-4·16·7
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-22)-6}{2*16}=\frac{16}{32}
=1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-22)+6}{2*16}=\frac{28}{32}
=7/8
$