6t+t^2/2=32

Solution for 6t+t^2/2=32 equation:

6t+t^2/2=32

We move all terms to the left:

6t+t^2/2-(32)=0

We multiply all the terms by the denominator


t^2+6t*2-32*2=0

We add all the numbers together, and all the variables

t^2+6t*2-64=0

Wy multiply elements

t^2+12t-64=0

a = 1; b = 12; c = -64;
Δ = b2-4ac
Δ = 122-4·1·(-64)
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-20}{2*1}=\frac{-32}{2}
=-16
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+20}{2*1}=\frac{8}{2}
=4
$