5/6w-13+1/4w=-1

Solution for 5/6w-13+1/4w=-1 equation:

5/6w-13+1/4w=-1

We move all terms to the left:

5/6w-13+1/4w-(-1)=0


Domain of the equation: 6w!=0

w!=0/6

w!=0

w∈R



Domain of the equation: 4w!=0

w!=0/4

w!=0

w∈R


We add all the numbers together, and all the variables

5/6w+1/4w-12=0

We calculate fractions


20w/24w^2+6w/24w^2-12=0

We multiply all the terms by the denominator


20w+6w-12*24w^2=0

We add all the numbers together, and all the variables

26w-12*24w^2=0

Wy multiply elements

-288w^2+26w=0

a = -288; b = 26; c = 0;
Δ = b2-4ac
Δ = 262-4·(-288)·0
Δ = 676
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{676}=26$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(26)-26}{2*-288}=\frac{-52}{-576}
=13/144
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(26)+26}{2*-288}=\frac{0}{-576}
=0
$