(2/7)*t=1/4

Solution for (2/7)*t=1/4 equation:

(2/7)*t=1/4

We move all terms to the left:

(2/7)*t-(1/4)=0


Domain of the equation: 7)*t!=0

t!=0/1

t!=0

t∈R


We add all the numbers together, and all the variables

(+2/7)*t-(+1/4)=0

We multiply parentheses

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

We get rid of parentheses

2t^2-1/4=0

We multiply all the terms by the denominator


2t^2*4-1=0

Wy multiply elements

8t^2-1=0

a = 8; b = 0; c = -1;
Δ = b2-4ac
Δ = 02-4·8·(-1)
Δ = 32
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:

$\sqrt{\Delta}=\sqrt{32}=\sqrt{16*2}=\sqrt{16}*\sqrt{2}=4\sqrt{2}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{2}}{2*8}=\frac{0-4\sqrt{2}}{16}
=-\frac{4\sqrt{2}}{16}
=-\frac{\sqrt{2}}{4}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{2}}{2*8}=\frac{0+4\sqrt{2}}{16}
=\frac{4\sqrt{2}}{16}
=\frac{\sqrt{2}}{4}
$