-4.9x^2-78x-150=0

Solution for -4.9x^2-78x-150=0 equation:

-4.9x^2-78x-150=0

a = -4.9; b = -78; c = -150;
Δ = b2-4ac
Δ = -782-4·(-4.9)·(-150)
Δ = 3144
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:

$\sqrt{\Delta}=\sqrt{3144}=\sqrt{4*786}=\sqrt{4}*\sqrt{786}=2\sqrt{786}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-78)-2\sqrt{786}}{2*-4.9}=\frac{78-2\sqrt{786}}{-9.8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-78)+2\sqrt{786}}{2*-4.9}=\frac{78+2\sqrt{786}}{-9.8}
$