12(t+7)+12t=t(t+7)

Solution for 12(t+7)+12t=t(t+7) equation:

12(t+7)+12t=t(t+7)

We move all terms to the left:

12(t+7)+12t-(t(t+7))=0

We add all the numbers together, and all the variables

12t+12(t+7)-(t(t+7))=0

We multiply parentheses

12t+12t-(t(t+7))+84=0


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

t(t+7)

We multiply parentheses

t^2+7t

Back to the equation:

-(t^2+7t)


We add all the numbers together, and all the variables

24t-(t^2+7t)+84=0

We get rid of parentheses

-t^2+24t-7t+84=0

We add all the numbers together, and all the variables

-1t^2+17t+84=0

a = -1; b = 17; c = +84;
Δ = b2-4ac
Δ = 172-4·(-1)·84
Δ = 625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{625}=25$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(17)-25}{2*-1}=\frac{-42}{-2}
=+21
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+25}{2*-1}=\frac{8}{-2}
=-4
$