-7/5t-2=-4-7t

Solution for -7/5t-2=-4-7t equation:

-7/5t-2=-4-7t

We move all terms to the left:

-7/5t-2-(-4-7t)=0


Domain of the equation: 5t!=0

t!=0/5

t!=0

t∈R


We add all the numbers together, and all the variables

-7/5t-(-7t-4)-2=0

We get rid of parentheses

-7/5t+7t+4-2=0

We multiply all the terms by the denominator


7t*5t+4*5t-2*5t-7=0

Wy multiply elements

35t^2+20t-10t-7=0

We add all the numbers together, and all the variables

35t^2+10t-7=0

a = 35; b = 10; c = -7;
Δ = b2-4ac
Δ = 102-4·35·(-7)
Δ = 1080
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:

$\sqrt{\Delta}=\sqrt{1080}=\sqrt{36*30}=\sqrt{36}*\sqrt{30}=6\sqrt{30}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-6\sqrt{30}}{2*35}=\frac{-10-6\sqrt{30}}{70}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+6\sqrt{30}}{2*35}=\frac{-10+6\sqrt{30}}{70}
$