1000=50t+70t(t-3)

Solution for 1000=50t+70t(t-3) equation:

1000=50t+70t(t-3)

We move all terms to the left:

1000-(50t+70t(t-3))=0


We calculate terms in parentheses: -(50t+70t(t-3)), so:

50t+70t(t-3)

We multiply parentheses

70t^2+50t-210t

We add all the numbers together, and all the variables

70t^2-160t

Back to the equation:

-(70t^2-160t)


We get rid of parentheses

-70t^2+160t+1000=0

a = -70; b = 160; c = +1000;
Δ = b2-4ac
Δ = 1602-4·(-70)·1000
Δ = 305600
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:

$\sqrt{\Delta}=\sqrt{305600}=\sqrt{1600*191}=\sqrt{1600}*\sqrt{191}=40\sqrt{191}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(160)-40\sqrt{191}}{2*-70}=\frac{-160-40\sqrt{191}}{-140}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(160)+40\sqrt{191}}{2*-70}=\frac{-160+40\sqrt{191}}{-140}
$