5w-12/w-7=0

Solution for 5w-12/w-7=0 equation:

5w-12/w-7=0


Domain of the equation: w!=0

w∈R


We multiply all the terms by the denominator


5w*w-7*w-12=0

We add all the numbers together, and all the variables

-7w+5w*w-12=0

Wy multiply elements

5w^2-7w-12=0

a = 5; b = -7; c = -12;
Δ = b2-4ac
Δ = -72-4·5·(-12)
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-17}{2*5}=\frac{-10}{10}
=-1
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+17}{2*5}=\frac{24}{10}
=2+2/5
$