4.90a^2-90a-150=0

Solution for 4.90a^2-90a-150=0 equation:

4.90a^2-90a-150=0

a = 4.90; b = -90; c = -150;
Δ = b2-4ac
Δ = -902-4·4.90·(-150)
Δ = 11040
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{11040}=\sqrt{16*690}=\sqrt{16}*\sqrt{690}=4\sqrt{690}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-90)-4\sqrt{690}}{2*4.90}=\frac{90-4\sqrt{690}}{9.8}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-90)+4\sqrt{690}}{2*4.90}=\frac{90+4\sqrt{690}}{9.8}
$