-16x^2+692x+42=1974

Solution for -16x^2+692x+42=1974 equation:

-16x^2+692x+42=1974

We move all terms to the left:

-16x^2+692x+42-(1974)=0

We add all the numbers together, and all the variables

-16x^2+692x-1932=0

a = -16; b = 692; c = -1932;
Δ = b2-4ac
Δ = 6922-4·(-16)·(-1932)
Δ = 355216
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{355216}=596$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(692)-596}{2*-16}=\frac{-1288}{-32}
=40+1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(692)+596}{2*-16}=\frac{-96}{-32}
=+3
$