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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

t^2+0.25t-3.5=0

a = 1; b = 0.25; c = -3.5;
Δ = b2-4ac
Δ = 0.252-4·1·(-3.5)
Δ = 14.0625
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{-(0.25)-\sqrt{14.0625}}{2*1}=\frac{-0.25-\sqrt{14.0625}}{2}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0.25)+\sqrt{14.0625}}{2*1}=\frac{-0.25+\sqrt{14.0625}}{2}
$