0=4.9x^2-68x-140

Solution for 0=4.9x^2-68x-140 equation:

0=4.9x^2-68x-140

We move all terms to the left:

0-(4.9x^2-68x-140)=0

We add all the numbers together, and all the variables

-(4.9x^2-68x-140)=0

We get rid of parentheses

-4.9x^2+68x+140=0

a = -4.9; b = 68; c = +140;
Δ = b2-4ac
Δ = 682-4·(-4.9)·140
Δ = 7368
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:

$\sqrt{\Delta}=\sqrt{7368}=\sqrt{4*1842}=\sqrt{4}*\sqrt{1842}=2\sqrt{1842}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(68)-2\sqrt{1842}}{2*-4.9}=\frac{-68-2\sqrt{1842}}{-9.8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(68)+2\sqrt{1842}}{2*-4.9}=\frac{-68+2\sqrt{1842}}{-9.8}
$