59=2x+9.8x^2/2

Solution for 59=2x+9.8x^2/2 equation:

59=2x+9.8x^2/2

We move all terms to the left:

59-(2x+9.8x^2/2)=0

We get rid of parentheses

-9.8x^2/2-2x+59=0

We multiply all the terms by the denominator


-9.8x^2-2x*2+59*2=0

We add all the numbers together, and all the variables

-9.8x^2-2x*2+118=0

Wy multiply elements

-9.8x^2-4x+118=0

a = -9.8; b = -4; c = +118;
Δ = b2-4ac
Δ = -42-4·(-9.8)·118
Δ = 4641.6
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-\sqrt{4641.6}}{2*-9.8}=\frac{4-\sqrt{4641.6}}{-19.6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+\sqrt{4641.6}}{2*-9.8}=\frac{4+\sqrt{4641.6}}{-19.6}
$