5/2w+8-12w=16-15w

Solution for 5/2w+8-12w=16-15w equation:

5/2w+8-12w=16-15w

We move all terms to the left:

5/2w+8-12w-(16-15w)=0


Domain of the equation: 2w!=0

w!=0/2

w!=0

w∈R


We add all the numbers together, and all the variables

5/2w-12w-(-15w+16)+8=0

We add all the numbers together, and all the variables

-12w+5/2w-(-15w+16)+8=0

We get rid of parentheses

-12w+5/2w+15w-16+8=0

We multiply all the terms by the denominator


-12w*2w+15w*2w-16*2w+8*2w+5=0

Wy multiply elements

-24w^2+30w^2-32w+16w+5=0

We add all the numbers together, and all the variables

6w^2-16w+5=0

a = 6; b = -16; c = +5;
Δ = b2-4ac
Δ = -162-4·6·5
Δ = 136
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:

$\sqrt{\Delta}=\sqrt{136}=\sqrt{4*34}=\sqrt{4}*\sqrt{34}=2\sqrt{34}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-2\sqrt{34}}{2*6}=\frac{16-2\sqrt{34}}{12}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+2\sqrt{34}}{2*6}=\frac{16+2\sqrt{34}}{12}
$