9t-21=3t(t-7)+6t

Solution for 9t-21=3t(t-7)+6t equation:

9t-21=3t(t-7)+6t

We move all terms to the left:

9t-21-(3t(t-7)+6t)=0


We calculate terms in parentheses: -(3t(t-7)+6t), so:

3t(t-7)+6t

We add all the numbers together, and all the variables

6t+3t(t-7)

We multiply parentheses

3t^2+6t-21t

We add all the numbers together, and all the variables

3t^2-15t

Back to the equation:

-(3t^2-15t)


We get rid of parentheses

-3t^2+9t+15t-21=0

We add all the numbers together, and all the variables

-3t^2+24t-21=0

a = -3; b = 24; c = -21;
Δ = b2-4ac
Δ = 242-4·(-3)·(-21)
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-18}{2*-3}=\frac{-42}{-6}
=+7
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+18}{2*-3}=\frac{-6}{-6}
=1
$