X^2-70x+500=0

Solution for X^2-70x+500=0 equation:

X^2-70X+500=0

a = 1; b = -70; c = +500;
Δ = b2-4ac
Δ = -702-4·1·500
Δ = 2900
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:

$\sqrt{\Delta}=\sqrt{2900}=\sqrt{100*29}=\sqrt{100}*\sqrt{29}=10\sqrt{29}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-70)-10\sqrt{29}}{2*1}=\frac{70-10\sqrt{29}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-70)+10\sqrt{29}}{2*1}=\frac{70+10\sqrt{29}}{2}
$