16-2t=3/2t+6

Solution for 16-2t=3/2t+6 equation:

16-2t=3/2t+6

We move all terms to the left:

16-2t-(3/2t+6)=0


Domain of the equation: 2t+6)!=0

t∈R


We get rid of parentheses

-2t-3/2t-6+16=0

We multiply all the terms by the denominator


-2t*2t-6*2t+16*2t-3=0

Wy multiply elements

-4t^2-12t+32t-3=0

We add all the numbers together, and all the variables

-4t^2+20t-3=0

a = -4; b = 20; c = -3;
Δ = b2-4ac
Δ = 202-4·(-4)·(-3)
Δ = 352
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:

$\sqrt{\Delta}=\sqrt{352}=\sqrt{16*22}=\sqrt{16}*\sqrt{22}=4\sqrt{22}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-4\sqrt{22}}{2*-4}=\frac{-20-4\sqrt{22}}{-8}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+4\sqrt{22}}{2*-4}=\frac{-20+4\sqrt{22}}{-8}
$