(14/5)+(1/4)t=7

Solution for (14/5)+(1/4)t=7 equation:

(14/5)+(1/4)t=7

We move all terms to the left:

(14/5)+(1/4)t-(7)=0


Domain of the equation: 4)t!=0

t!=0/1

t!=0

t∈R


determiningTheFunctionDomain
(1/4)t-7+(14/5)=0

We add all the numbers together, and all the variables

(+1/4)t-7+(+14/5)=0

We multiply parentheses

t^2-7+(+14/5)=0

We get rid of parentheses

t^2-7+14/5=0

We multiply all the terms by the denominator


t^2*5+14-7*5=0

We add all the numbers together, and all the variables

t^2*5-21=0

Wy multiply elements

5t^2-21=0

a = 5; b = 0; c = -21;
Δ = b2-4ac
Δ = 02-4·5·(-21)
Δ = 420
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:

$\sqrt{\Delta}=\sqrt{420}=\sqrt{4*105}=\sqrt{4}*\sqrt{105}=2\sqrt{105}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{105}}{2*5}=\frac{0-2\sqrt{105}}{10}
=-\frac{2\sqrt{105}}{10}
=-\frac{\sqrt{105}}{5}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{105}}{2*5}=\frac{0+2\sqrt{105}}{10}
=\frac{2\sqrt{105}}{10}
=\frac{\sqrt{105}}{5}
$