2+23x-16x^2=10

Solution for 2+23x-16x^2=10 equation:

2+23x-16x^2=10

We move all terms to the left:

2+23x-16x^2-(10)=0

We add all the numbers together, and all the variables

-16x^2+23x-8=0

a = -16; b = 23; c = -8;
Δ = b2-4ac
Δ = 232-4·(-16)·(-8)
Δ = 17
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{-(23)-\sqrt{17}}{2*-16}=\frac{-23-\sqrt{17}}{-32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(23)+\sqrt{17}}{2*-16}=\frac{-23+\sqrt{17}}{-32}
$