7/10w-2/15w+1=0

Solution for 7/10w-2/15w+1=0 equation:

7/10w-2/15w+1=0


Domain of the equation: 10w!=0

w!=0/10

w!=0

w∈R



Domain of the equation: 15w!=0

w!=0/15

w!=0

w∈R


We calculate fractions


105w/150w^2+(-20w)/150w^2+1=0

We multiply all the terms by the denominator


105w+(-20w)+1*150w^2=0

Wy multiply elements

150w^2+105w+(-20w)=0

We get rid of parentheses

150w^2+105w-20w=0

We add all the numbers together, and all the variables

150w^2+85w=0

a = 150; b = 85; c = 0;
Δ = b2-4ac
Δ = 852-4·150·0
Δ = 7225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{7225}=85$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(85)-85}{2*150}=\frac{-170}{300}
=-17/30
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(85)+85}{2*150}=\frac{0}{300}
=0
$