1/2t+1/4t=5

Solution for 1/2t+1/4t=5 equation:

1/2t+1/4t=5

We move all terms to the left:

1/2t+1/4t-(5)=0


Domain of the equation: 2t!=0

t!=0/2

t!=0

t∈R



Domain of the equation: 4t!=0

t!=0/4

t!=0

t∈R


We calculate fractions


4t/8t^2+2t/8t^2-5=0

We multiply all the terms by the denominator


4t+2t-5*8t^2=0

We add all the numbers together, and all the variables

6t-5*8t^2=0

Wy multiply elements

-40t^2+6t=0

a = -40; b = 6; c = 0;
Δ = b2-4ac
Δ = 62-4·(-40)·0
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-6}{2*-40}=\frac{-12}{-80}
=3/20
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6}{2*-40}=\frac{0}{-80}
=0
$