(7/2t)=4+7t

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

(7/2t)=4+7t

We move all terms to the left:

(7/2t)-(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)=0

We get rid of parentheses

7/2t-7t-4=0

We multiply all the terms by the denominator


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

Wy multiply elements

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

a = -14; b = -8; c = +7;
Δ = b2-4ac
Δ = -82-4·(-14)·7
Δ = 456
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:

$\sqrt{\Delta}=\sqrt{456}=\sqrt{4*114}=\sqrt{4}*\sqrt{114}=2\sqrt{114}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-2\sqrt{114}}{2*-14}=\frac{8-2\sqrt{114}}{-28}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+2\sqrt{114}}{2*-14}=\frac{8+2\sqrt{114}}{-28}
$