w^2-70w+140=0

Solution for w^2-70w+140=0 equation:

w^2-70w+140=0

a = 1; b = -70; c = +140;
Δ = b2-4ac
Δ = -702-4·1·140
Δ = 4340
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{4340}=\sqrt{4*1085}=\sqrt{4}*\sqrt{1085}=2\sqrt{1085}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-70)-2\sqrt{1085}}{2*1}=\frac{70-2\sqrt{1085}}{2}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-70)+2\sqrt{1085}}{2*1}=\frac{70+2\sqrt{1085}}{2}
$