0.5t+.25t(t+16)=4+.75t

Solution for 0.5t+.25t(t+16)=4+.75t equation:

0.5t+.25t(t+16)=4+.75t

We move all terms to the left:

0.5t+.25t(t+16)-(4+.75t)=0

We add all the numbers together, and all the variables

0.5t+.25t(t+16)-(.75t+4)=0

We multiply parentheses

t^2+0.5t+16t-(.75t+4)=0

We get rid of parentheses

t^2+0.5t+16t-.75t-4=0

We add all the numbers together, and all the variables

t^2+15.75t-4=0

a = 1; b = 15.75; c = -4;
Δ = b2-4ac
Δ = 15.752-4·1·(-4)
Δ = 264.0625
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{-(15.75)-\sqrt{264.0625}}{2*1}=\frac{-15.75-\sqrt{264.0625}}{2}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15.75)+\sqrt{264.0625}}{2*1}=\frac{-15.75+\sqrt{264.0625}}{2}
$