t^2-30-200=0

Solution for t^2-30-200=0 equation:

t^2-30-200=0

We add all the numbers together, and all the variables

t^2-230=0

a = 1; b = 0; c = -230;
Δ = b2-4ac
Δ = 02-4·1·(-230)
Δ = 920
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{920}=\sqrt{4*230}=\sqrt{4}*\sqrt{230}=2\sqrt{230}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{230}}{2*1}=\frac{0-2\sqrt{230}}{2}
=-\frac{2\sqrt{230}}{2}
=-\sqrt{230}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{230}}{2*1}=\frac{0+2\sqrt{230}}{2}
=\frac{2\sqrt{230}}{2}
=\sqrt{230}
$