6w-10/w-5=1

Solution for 6w-10/w-5=1 equation:

6w-10/w-5=1

We move all terms to the left:

6w-10/w-5-(1)=0


Domain of the equation: w!=0

w∈R


We add all the numbers together, and all the variables

6w-10/w-6=0

We multiply all the terms by the denominator


6w*w-6*w-10=0

We add all the numbers together, and all the variables

-6w+6w*w-10=0

Wy multiply elements

6w^2-6w-10=0

a = 6; b = -6; c = -10;
Δ = b2-4ac
Δ = -62-4·6·(-10)
Δ = 276
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{276}=\sqrt{4*69}=\sqrt{4}*\sqrt{69}=2\sqrt{69}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{69}}{2*6}=\frac{6-2\sqrt{69}}{12}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{69}}{2*6}=\frac{6+2\sqrt{69}}{12}
$