120(t)=1/2t+3

Solution for 120(t)=1/2t+3 equation:

120(t)=1/2t+3

We move all terms to the left:

120(t)-(1/2t+3)=0


Domain of the equation: 2t+3)!=0

t∈R


We get rid of parentheses

120t-1/2t-3=0

We multiply all the terms by the denominator


120t*2t-3*2t-1=0

Wy multiply elements

240t^2-6t-1=0

a = 240; b = -6; c = -1;
Δ = b2-4ac
Δ = -62-4·240·(-1)
Δ = 996
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{996}=\sqrt{4*249}=\sqrt{4}*\sqrt{249}=2\sqrt{249}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{249}}{2*240}=\frac{6-2\sqrt{249}}{480}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{249}}{2*240}=\frac{6+2\sqrt{249}}{480}
$