32=18x+1/2*9.81x^2

Solution for 32=18x+1/2*9.81x^2 equation:

32=18x+1/2*9.81x^2

We move all terms to the left:

32-(18x+1/2*9.81x^2)=0


Domain of the equation: 2*9.81x^2)!=0

x!=0/1

x!=0

x∈R


We get rid of parentheses

-18x-1/2*9.81x^2+32=0

We multiply all the terms by the denominator


-18x*2*9.81x^2+32*2*9.81x^2-1=0

Wy multiply elements

-324x^2*9+576x*9-1=0

Wy multiply elements

-2916x^2+5184x-1=0

a = -2916; b = 5184; c = -1;
Δ = b2-4ac
Δ = 51842-4·(-2916)·(-1)
Δ = 26862192
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:

$\sqrt{\Delta}=\sqrt{26862192}=\sqrt{571536*47}=\sqrt{571536}*\sqrt{47}=756\sqrt{47}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5184)-756\sqrt{47}}{2*-2916}=\frac{-5184-756\sqrt{47}}{-5832}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5184)+756\sqrt{47}}{2*-2916}=\frac{-5184+756\sqrt{47}}{-5832}
$