8x^2-5x-2100=0

Solution for 8x^2-5x-2100=0 equation:

8x^2-5x-2100=0

a = 8; b = -5; c = -2100;
Δ = b2-4ac
Δ = -52-4·8·(-2100)
Δ = 67225
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:

$\sqrt{\Delta}=\sqrt{67225}=\sqrt{25*2689}=\sqrt{25}*\sqrt{2689}=5\sqrt{2689}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-5\sqrt{2689}}{2*8}=\frac{5-5\sqrt{2689}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+5\sqrt{2689}}{2*8}=\frac{5+5\sqrt{2689}}{16}
$