10a^2-10a-2000=0

Solution for 10a^2-10a-2000=0 equation:

10a^2-10a-2000=0

a = 10; b = -10; c = -2000;
Δ = b2-4ac
Δ = -102-4·10·(-2000)
Δ = 80100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{80100}=\sqrt{900*89}=\sqrt{900}*\sqrt{89}=30\sqrt{89}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-30\sqrt{89}}{2*10}=\frac{10-30\sqrt{89}}{20}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+30\sqrt{89}}{2*10}=\frac{10+30\sqrt{89}}{20}
$