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

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

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

We move all terms to the left:

7/2t-2-(4t+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-(+8t)-2=0

We get rid of parentheses

7/2t-8t-2=0

We multiply all the terms by the denominator


-8t*2t-2*2t+7=0

Wy multiply elements

-16t^2-4t+7=0

a = -16; b = -4; c = +7;
Δ = b2-4ac
Δ = -42-4·(-16)·7
Δ = 464
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:

$\sqrt{\Delta}=\sqrt{464}=\sqrt{16*29}=\sqrt{16}*\sqrt{29}=4\sqrt{29}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4\sqrt{29}}{2*-16}=\frac{4-4\sqrt{29}}{-32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4\sqrt{29}}{2*-16}=\frac{4+4\sqrt{29}}{-32}
$