0=700-140x+0.5x^2

Solution for 0=700-140x+0.5x^2 equation:

0=700-140x+0.5x^2

We move all terms to the left:

0-(700-140x+0.5x^2)=0

We add all the numbers together, and all the variables

-(700-140x+0.5x^2)=0

We get rid of parentheses

-0.5x^2+140x-700=0

a = -0.5; b = 140; c = -700;
Δ = b2-4ac
Δ = 1402-4·(-0.5)·(-700)
Δ = 18200
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:

$\sqrt{\Delta}=\sqrt{18200}=\sqrt{100*182}=\sqrt{100}*\sqrt{182}=10\sqrt{182}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(140)-10\sqrt{182}}{2*-0.5}=\frac{-140-10\sqrt{182}}{-1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(140)+10\sqrt{182}}{2*-0.5}=\frac{-140+10\sqrt{182}}{-1}
$