108(t-20)+108t=t(t-20)

Solution for 108(t-20)+108t=t(t-20) equation:

108(t-20)+108t=t(t-20)

We move all terms to the left:

108(t-20)+108t-(t(t-20))=0

We add all the numbers together, and all the variables

108t+108(t-20)-(t(t-20))=0

We multiply parentheses

108t+108t-(t(t-20))-2160=0


We calculate terms in parentheses: -(t(t-20)), so:

t(t-20)

We multiply parentheses

t^2-20t

Back to the equation:

-(t^2-20t)


We add all the numbers together, and all the variables

216t-(t^2-20t)-2160=0

We get rid of parentheses

-t^2+216t+20t-2160=0

We add all the numbers together, and all the variables

-1t^2+236t-2160=0

a = -1; b = 236; c = -2160;
Δ = b2-4ac
Δ = 2362-4·(-1)·(-2160)
Δ = 47056
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:

$\sqrt{\Delta}=\sqrt{47056}=\sqrt{16*2941}=\sqrt{16}*\sqrt{2941}=4\sqrt{2941}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(236)-4\sqrt{2941}}{2*-1}=\frac{-236-4\sqrt{2941}}{-2}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(236)+4\sqrt{2941}}{2*-1}=\frac{-236+4\sqrt{2941}}{-2}
$