X2-30x-2000=0

Solution for X2-30x-2000=0 equation:

X2-30X-2000=0

We add all the numbers together, and all the variables

X^2-30X-2000=0

a = 1; b = -30; c = -2000;
Δ = b2-4ac
Δ = -302-4·1·(-2000)
Δ = 8900
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:

$\sqrt{\Delta}=\sqrt{8900}=\sqrt{100*89}=\sqrt{100}*\sqrt{89}=10\sqrt{89}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-10\sqrt{89}}{2*1}=\frac{30-10\sqrt{89}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+10\sqrt{89}}{2*1}=\frac{30+10\sqrt{89}}{2}
$