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

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

7/2t-2=4+4t

We move all terms to the left:

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

We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

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

We add all the numbers together, and all the variables

-8t^2-12t+7=0

a = -8; b = -12; c = +7;
Δ = b2-4ac
Δ = -122-4·(-8)·7
Δ = 368
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:

$\sqrt{\Delta}=\sqrt{368}=\sqrt{16*23}=\sqrt{16}*\sqrt{23}=4\sqrt{23}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-4\sqrt{23}}{2*-8}=\frac{12-4\sqrt{23}}{-16}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+4\sqrt{23}}{2*-8}=\frac{12+4\sqrt{23}}{-16}
$