-4.9x^2+48x=-200

Solution for -4.9x^2+48x=-200 equation:

-4.9x^2+48x=-200

We move all terms to the left:

-4.9x^2+48x-(-200)=0

We add all the numbers together, and all the variables

-4.9x^2+48x+200=0

a = -4.9; b = 48; c = +200;
Δ = b2-4ac
Δ = 482-4·(-4.9)·200
Δ = 6224
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:

$\sqrt{\Delta}=\sqrt{6224}=\sqrt{16*389}=\sqrt{16}*\sqrt{389}=4\sqrt{389}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(48)-4\sqrt{389}}{2*-4.9}=\frac{-48-4\sqrt{389}}{-9.8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(48)+4\sqrt{389}}{2*-4.9}=\frac{-48+4\sqrt{389}}{-9.8}
$