35x^2-5x-5000=0

Solution for 35x^2-5x-5000=0 equation:

35x^2-5x-5000=0

a = 35; b = -5; c = -5000;
Δ = b2-4ac
Δ = -52-4·35·(-5000)
Δ = 700025
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:

$\sqrt{\Delta}=\sqrt{700025}=\sqrt{25*28001}=\sqrt{25}*\sqrt{28001}=5\sqrt{28001}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-5\sqrt{28001}}{2*35}=\frac{5-5\sqrt{28001}}{70}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+5\sqrt{28001}}{2*35}=\frac{5+5\sqrt{28001}}{70}
$