100=15+10t^2/2

Solution for 100=15+10t^2/2 equation:

100=15+10t^2/2

We move all terms to the left:

100-(15+10t^2/2)=0

We get rid of parentheses

-10t^2/2-15+100=0

We multiply all the terms by the denominator


-10t^2-15*2+100*2=0

We add all the numbers together, and all the variables

-10t^2+170=0

a = -10; b = 0; c = +170;
Δ = b2-4ac
Δ = 02-4·(-10)·170
Δ = 6800
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:

$\sqrt{\Delta}=\sqrt{6800}=\sqrt{400*17}=\sqrt{400}*\sqrt{17}=20\sqrt{17}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-20\sqrt{17}}{2*-10}=\frac{0-20\sqrt{17}}{-20}
=-\frac{20\sqrt{17}}{-20}
=-\frac{\sqrt{17}}{-1}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+20\sqrt{17}}{2*-10}=\frac{0+20\sqrt{17}}{-20}
=\frac{20\sqrt{17}}{-20}
=\frac{\sqrt{17}}{-1}
$