3+90x-16x^2=84

Solution for 3+90x-16x^2=84 equation:

3+90x-16x^2=84

We move all terms to the left:

3+90x-16x^2-(84)=0

We add all the numbers together, and all the variables

-16x^2+90x-81=0

a = -16; b = 90; c = -81;
Δ = b2-4ac
Δ = 902-4·(-16)·(-81)
Δ = 2916
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2916}=54$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(90)-54}{2*-16}=\frac{-144}{-32}
=4+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(90)+54}{2*-16}=\frac{-36}{-32}
=1+1/8
$