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

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

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

We move all terms to the left:

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


Domain of the equation: 4t!=0

t!=0/4

t!=0

t∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

28t^2+16t-8t-2=0

We add all the numbers together, and all the variables

28t^2+8t-2=0

a = 28; b = 8; c = -2;
Δ = b2-4ac
Δ = 82-4·28·(-2)
Δ = 288
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:

$\sqrt{\Delta}=\sqrt{288}=\sqrt{144*2}=\sqrt{144}*\sqrt{2}=12\sqrt{2}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-12\sqrt{2}}{2*28}=\frac{-8-12\sqrt{2}}{56}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+12\sqrt{2}}{2*28}=\frac{-8+12\sqrt{2}}{56}
$