40x+5=4.9x^2

Solution for 40x+5=4.9x^2 equation:

40x+5=4.9x^2

We move all terms to the left:

40x+5-(4.9x^2)=0

We get rid of parentheses

-4.9x^2+40x+5=0

a = -4.9; b = 40; c = +5;
Δ = b2-4ac
Δ = 402-4·(-4.9)·5
Δ = 1698
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{-(40)-\sqrt{1698}}{2*-4.9}=\frac{-40-\sqrt{1698}}{-9.8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+\sqrt{1698}}{2*-4.9}=\frac{-40+\sqrt{1698}}{-9.8}
$