7/2*t+2=4+7t

Solution for 7/2*t+2=4+7t equation:

7/2t+2=4+7t

We move all terms to the left:

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


Domain of the equation: 2t!=0

t!=0/2

t!=0

t∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

7/2t-7t-4+2=0

We multiply all the terms by the denominator


-7t*2t-4*2t+2*2t+7=0

Wy multiply elements

-14t^2-8t+4t+7=0

We add all the numbers together, and all the variables

-14t^2-4t+7=0

a = -14; b = -4; c = +7;
Δ = b2-4ac
Δ = -42-4·(-14)·7
Δ = 408
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:

$\sqrt{\Delta}=\sqrt{408}=\sqrt{4*102}=\sqrt{4}*\sqrt{102}=2\sqrt{102}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-2\sqrt{102}}{2*-14}=\frac{4-2\sqrt{102}}{-28}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+2\sqrt{102}}{2*-14}=\frac{4+2\sqrt{102}}{-28}
$