4.9x^2-14x-45=0

Solution for 4.9x^2-14x-45=0 equation:

4.9x^2-14x-45=0

a = 4.9; b = -14; c = -45;
Δ = b2-4ac
Δ = -142-4·4.9·(-45)
Δ = 1078
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:

$\sqrt{\Delta}=\sqrt{1078}=\sqrt{49*22}=\sqrt{49}*\sqrt{22}=7\sqrt{22}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-7\sqrt{22}}{2*4.9}=\frac{14-7\sqrt{22}}{9.8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+7\sqrt{22}}{2*4.9}=\frac{14+7\sqrt{22}}{9.8}
$