-1/7t+9=10+5/14t

Solution for -1/7t+9=10+5/14t equation:

-1/7t+9=10+5/14t

We move all terms to the left:

-1/7t+9-(10+5/14t)=0


Domain of the equation: 7t!=0

t!=0/7

t!=0

t∈R



Domain of the equation: 14t)!=0

t!=0/1

t!=0

t∈R


We add all the numbers together, and all the variables

-1/7t-(5/14t+10)+9=0

We get rid of parentheses

-1/7t-5/14t-10+9=0

We calculate fractions


(-14t)/98t^2+(-35t)/98t^2-10+9=0

We add all the numbers together, and all the variables

(-14t)/98t^2+(-35t)/98t^2-1=0

We multiply all the terms by the denominator


(-14t)+(-35t)-1*98t^2=0

Wy multiply elements

-98t^2+(-14t)+(-35t)=0

We get rid of parentheses

-98t^2-14t-35t=0

We add all the numbers together, and all the variables

-98t^2-49t=0

a = -98; b = -49; c = 0;
Δ = b2-4ac
Δ = -492-4·(-98)·0
Δ = 2401
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2401}=49$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-49)-49}{2*-98}=\frac{0}{-196}
=0
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-49)+49}{2*-98}=\frac{98}{-196}
=-1/2
$