-16x^2+30x+31=42

Solution for -16x^2+30x+31=42 equation:

-16x^2+30x+31=42

We move all terms to the left:

-16x^2+30x+31-(42)=0

We add all the numbers together, and all the variables

-16x^2+30x-11=0

a = -16; b = 30; c = -11;
Δ = b2-4ac
Δ = 302-4·(-16)·(-11)
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-14}{2*-16}=\frac{-44}{-32}
=1+3/8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+14}{2*-16}=\frac{-16}{-32}
=1/2
$