t(t+6)=4(t+6)+4t

Solution for t(t+6)=4(t+6)+4t equation:

t(t+6)=4(t+6)+4t

We move all terms to the left:

t(t+6)-(4(t+6)+4t)=0

We multiply parentheses

t^2+6t-(4(t+6)+4t)=0


We calculate terms in parentheses: -(4(t+6)+4t), so:

4(t+6)+4t

We add all the numbers together, and all the variables

4t+4(t+6)

We multiply parentheses

4t+4t+24

We add all the numbers together, and all the variables

8t+24

Back to the equation:

-(8t+24)


We get rid of parentheses

t^2+6t-8t-24=0

We add all the numbers together, and all the variables

t^2-2t-24=0

a = 1; b = -2; c = -24;
Δ = b2-4ac
Δ = -22-4·1·(-24)
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-10}{2*1}=\frac{-8}{2}
=-4
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+10}{2*1}=\frac{12}{2}
=6
$