1/4t+2/3t=5

Solution for 1/4t+2/3t=5 equation:

1/4t+2/3t=5

We move all terms to the left:

1/4t+2/3t-(5)=0


Domain of the equation: 4t!=0

t!=0/4

t!=0

t∈R



Domain of the equation: 3t!=0

t!=0/3

t!=0

t∈R


We calculate fractions


3t/12t^2+8t/12t^2-5=0

We multiply all the terms by the denominator


3t+8t-5*12t^2=0

We add all the numbers together, and all the variables

11t-5*12t^2=0

Wy multiply elements

-60t^2+11t=0

a = -60; b = 11; c = 0;
Δ = b2-4ac
Δ = 112-4·(-60)·0
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-11}{2*-60}=\frac{-22}{-120}
=11/60
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+11}{2*-60}=\frac{0}{-120}
=0
$