(-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!=0/2

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

We add all the numbers together, and all the variables

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}
$