-5(2-w)+7/3w-12/3=

Solution for -5(2-w)+7/3w-12/3= equation:

-5(2-w)+7/3w-12/3=

We move all terms to the left:

-5(2-w)+7/3w-12/3-()=0


Domain of the equation: 3w!=0

w!=0/3

w!=0

w∈R


We add all the numbers together, and all the variables

-5(-1w+2)+7/3w-12/3-()=0

We add all the numbers together, and all the variables

-5(-1w+2)+7/3w=0

We multiply parentheses

5w+7/3w-10=0

We multiply all the terms by the denominator


5w*3w-10*3w+7=0

Wy multiply elements

15w^2-30w+7=0

a = 15; b = -30; c = +7;
Δ = b2-4ac
Δ = -302-4·15·7
Δ = 480
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:

$\sqrt{\Delta}=\sqrt{480}=\sqrt{16*30}=\sqrt{16}*\sqrt{30}=4\sqrt{30}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-4\sqrt{30}}{2*15}=\frac{30-4\sqrt{30}}{30}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+4\sqrt{30}}{2*15}=\frac{30+4\sqrt{30}}{30}
$