-7/2t-2=-2-7t

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

-7/2t-2=-2-7t

We move all terms to the left:

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

We get rid of parentheses

-7/2t+7t+2-2=0

We multiply all the terms by the denominator


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

Wy multiply elements

14t^2+4t-4t-7=0

We add all the numbers together, and all the variables

14t^2-7=0

a = 14; b = 0; c = -7;
Δ = b2-4ac
Δ = 02-4·14·(-7)
Δ = 392
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:

$\sqrt{\Delta}=\sqrt{392}=\sqrt{196*2}=\sqrt{196}*\sqrt{2}=14\sqrt{2}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-14\sqrt{2}}{2*14}=\frac{0-14\sqrt{2}}{28}
=-\frac{14\sqrt{2}}{28}
=-\frac{\sqrt{2}}{2}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+14\sqrt{2}}{2*14}=\frac{0+14\sqrt{2}}{28}
=\frac{14\sqrt{2}}{28}
=\frac{\sqrt{2}}{2}
$