15(t)=5t^2+30t+10

Solution for 15(t)=5t^2+30t+10 equation:

15(t)=5t^2+30t+10

We move all terms to the left:

15(t)-(5t^2+30t+10)=0

We get rid of parentheses

-5t^2+15t-30t-10=0

We add all the numbers together, and all the variables

-5t^2-15t-10=0

a = -5; b = -15; c = -10;
Δ = b2-4ac
Δ = -152-4·(-5)·(-10)
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-5}{2*-5}=\frac{10}{-10}
=-1
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+5}{2*-5}=\frac{20}{-10}
=-2
$