1/2t+4t=-15

Solution for 1/2t+4t=-15 equation:

1/2t+4t=-15

We move all terms to the left:

1/2t+4t-(-15)=0


Domain of the equation: 2t!=0

t!=0/2

t!=0

t∈R


We add all the numbers together, and all the variables

4t+1/2t+15=0

We multiply all the terms by the denominator


4t*2t+15*2t+1=0

Wy multiply elements

8t^2+30t+1=0

a = 8; b = 30; c = +1;
Δ = b2-4ac
Δ = 302-4·8·1
Δ = 868
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:

$\sqrt{\Delta}=\sqrt{868}=\sqrt{4*217}=\sqrt{4}*\sqrt{217}=2\sqrt{217}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-2\sqrt{217}}{2*8}=\frac{-30-2\sqrt{217}}{16}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+2\sqrt{217}}{2*8}=\frac{-30+2\sqrt{217}}{16}
$