7/10w-18=1w

Solution for 7/10w-18=1w equation:

7/10w-18=1w

We move all terms to the left:

7/10w-18-(1w)=0


Domain of the equation: 10w!=0

w!=0/10

w!=0

w∈R


We add all the numbers together, and all the variables

-1w+7/10w-18=0

We multiply all the terms by the denominator


-1w*10w-18*10w+7=0

Wy multiply elements

-10w^2-180w+7=0

a = -10; b = -180; c = +7;
Δ = b2-4ac
Δ = -1802-4·(-10)·7
Δ = 32680
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:

$\sqrt{\Delta}=\sqrt{32680}=\sqrt{4*8170}=\sqrt{4}*\sqrt{8170}=2\sqrt{8170}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-180)-2\sqrt{8170}}{2*-10}=\frac{180-2\sqrt{8170}}{-20}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-180)+2\sqrt{8170}}{2*-10}=\frac{180+2\sqrt{8170}}{-20}
$