1/5t+2-t=17

Solution for 1/5t+2-t=17 equation:

1/5t+2-t=17

We move all terms to the left:

1/5t+2-t-(17)=0


Domain of the equation: 5t!=0

t!=0/5

t!=0

t∈R


We add all the numbers together, and all the variables

-1t+1/5t-15=0

We multiply all the terms by the denominator


-1t*5t-15*5t+1=0

Wy multiply elements

-5t^2-75t+1=0

a = -5; b = -75; c = +1;
Δ = b2-4ac
Δ = -752-4·(-5)·1
Δ = 5645
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-75)-\sqrt{5645}}{2*-5}=\frac{75-\sqrt{5645}}{-10}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-75)+\sqrt{5645}}{2*-5}=\frac{75+\sqrt{5645}}{-10}
$