0.5t+0.25t(t+16)=4+0.75t

Solution for 0.5t+0.25t(t+16)=4+0.75t equation:

0.5t+0.25t(t+16)=4+0.75t

We move all terms to the left:

0.5t+0.25t(t+16)-(4+0.75t)=0

We add all the numbers together, and all the variables

0.5t+0.25t(t+16)-(0.75t+4)=0

We multiply parentheses

0t^2+0.5t+0t-(0.75t+4)=0

We get rid of parentheses

0t^2+0.5t+0t-0.75t-4=0

We add all the numbers together, and all the variables

t^2+0.75t-4=0

a = 1; b = 0.75; c = -4;
Δ = b2-4ac
Δ = 0.752-4·1·(-4)
Δ = 16.5625
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{-(0.75)-\sqrt{16.5625}}{2*1}=\frac{-0.75-\sqrt{16.5625}}{2}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0.75)+\sqrt{16.5625}}{2*1}=\frac{-0.75+\sqrt{16.5625}}{2}
$