40t=50t(t-1/2)

Solution for 40t=50t(t-1/2) equation:

40t=50t(t-1/2)

We move all terms to the left:

40t-(50t(t-1/2))=0

We add all the numbers together, and all the variables

40t-(50t(+t-1/2))=0

We multiply all the terms by the denominator


40t*2))-(50t(+t-1=0

We add all the numbers together, and all the variables

t+40t*2))-(50t(-1=0

Wy multiply elements

80t^2+t-1=0

a = 80; b = 1; c = -1;
Δ = b2-4ac
Δ = 12-4·80·(-1)
Δ = 321
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-\sqrt{321}}{2*80}=\frac{-1-\sqrt{321}}{160}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{321}}{2*80}=\frac{-1+\sqrt{321}}{160}
$