-16x^2+158x+7=197

Solution for -16x^2+158x+7=197 equation:

-16x^2+158x+7=197

We move all terms to the left:

-16x^2+158x+7-(197)=0

We add all the numbers together, and all the variables

-16x^2+158x-190=0

a = -16; b = 158; c = -190;
Δ = b2-4ac
Δ = 1582-4·(-16)·(-190)
Δ = 12804
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{12804}=\sqrt{4*3201}=\sqrt{4}*\sqrt{3201}=2\sqrt{3201}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(158)-2\sqrt{3201}}{2*-16}=\frac{-158-2\sqrt{3201}}{-32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(158)+2\sqrt{3201}}{2*-16}=\frac{-158+2\sqrt{3201}}{-32}
$