9t=(60-t)*0.75t

Solution for 9t=(60-t)*0.75t equation:

9t=(60-t)*0.75t

We move all terms to the left:

9t-((60-t)*0.75t)=0

We add all the numbers together, and all the variables

9t-((-1t+60)*0.75t)=0


We calculate terms in parentheses: -((-1t+60)*0.75t), so:

(-1t+60)*0.75t

We multiply parentheses

0t^2+0t

We add all the numbers together, and all the variables

t^2+t

Back to the equation:

-(t^2+t)


We get rid of parentheses

-t^2+9t-t=0

We add all the numbers together, and all the variables

-1t^2+8t=0

a = -1; b = 8; c = 0;
Δ = b2-4ac
Δ = 82-4·(-1)·0
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-8}{2*-1}=\frac{-16}{-2}
=+8
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+8}{2*-1}=\frac{0}{-2}
=0
$