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

Solution for ((7)/(2)t)-2=4+7t equation:

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

We move all terms to the left:

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


Domain of the equation: 2t)!=0

t!=0/1

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^2-12t+7=0

a = -14; b = -12; c = +7;
Δ = b2-4ac
Δ = -122-4·(-14)·7
Δ = 536
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:

$\sqrt{\Delta}=\sqrt{536}=\sqrt{4*134}=\sqrt{4}*\sqrt{134}=2\sqrt{134}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-2\sqrt{134}}{2*-14}=\frac{12-2\sqrt{134}}{-28}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+2\sqrt{134}}{2*-14}=\frac{12+2\sqrt{134}}{-28}
$