(1/4)+(1/2)t=4

Solution for (1/4)+(1/2)t=4 equation:

(1/4)+(1/2)t=4

We move all terms to the left:

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


Domain of the equation: 2)t!=0

t!=0/1

t!=0

t∈R


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

We add all the numbers together, and all the variables

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

We multiply parentheses

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

We get rid of parentheses

t^2-4+1/4=0

We multiply all the terms by the denominator


t^2*4+1-4*4=0

We add all the numbers together, and all the variables

t^2*4-15=0

Wy multiply elements

4t^2-15=0

a = 4; b = 0; c = -15;
Δ = b2-4ac
Δ = 02-4·4·(-15)
Δ = 240
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:

$\sqrt{\Delta}=\sqrt{240}=\sqrt{16*15}=\sqrt{16}*\sqrt{15}=4\sqrt{15}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{15}}{2*4}=\frac{0-4\sqrt{15}}{8}
=-\frac{4\sqrt{15}}{8}
=-\frac{\sqrt{15}}{2}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{15}}{2*4}=\frac{0+4\sqrt{15}}{8}
=\frac{4\sqrt{15}}{8}
=\frac{\sqrt{15}}{2}
$