0=-4.9x^2+14x-5

Solution for 0=-4.9x^2+14x-5 equation:

0=-4.9x^2+14x-5

We move all terms to the left:

0-(-4.9x^2+14x-5)=0

We add all the numbers together, and all the variables

-(-4.9x^2+14x-5)=0

We get rid of parentheses

4.9x^2-14x+5=0

a = 4.9; b = -14; c = +5;
Δ = b2-4ac
Δ = -142-4·4.9·5
Δ = 98
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:

$\sqrt{\Delta}=\sqrt{98}=\sqrt{49*2}=\sqrt{49}*\sqrt{2}=7\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-7\sqrt{2}}{2*4.9}=\frac{14-7\sqrt{2}}{9.8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+7\sqrt{2}}{2*4.9}=\frac{14+7\sqrt{2}}{9.8}
$