10=154-10t-16t2

Solution for 10=154-10t-16t2 equation:

10=154-10t-16t^2

We move all terms to the left:

10-(154-10t-16t^2)=0

We get rid of parentheses

16t^2+10t-154+10=0

We add all the numbers together, and all the variables

16t^2+10t-144=0

a = 16; b = 10; c = -144;
Δ = b2-4ac
Δ = 102-4·16·(-144)
Δ = 9316
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:

$\sqrt{\Delta}=\sqrt{9316}=\sqrt{4*2329}=\sqrt{4}*\sqrt{2329}=2\sqrt{2329}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{2329}}{2*16}=\frac{-10-2\sqrt{2329}}{32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{2329}}{2*16}=\frac{-10+2\sqrt{2329}}{32}
$