7/10w-18=26w

Solution for 7/10w-18=26w equation:

7/10w-18=26w

We move all terms to the left:

7/10w-18-(26w)=0


Domain of the equation: 10w!=0

w!=0/10

w!=0

w∈R


We add all the numbers together, and all the variables

-26w+7/10w-18=0

We multiply all the terms by the denominator


-26w*10w-18*10w+7=0

Wy multiply elements

-260w^2-180w+7=0

a = -260; b = -180; c = +7;
Δ = b2-4ac
Δ = -1802-4·(-260)·7
Δ = 39680
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:

$\sqrt{\Delta}=\sqrt{39680}=\sqrt{256*155}=\sqrt{256}*\sqrt{155}=16\sqrt{155}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-180)-16\sqrt{155}}{2*-260}=\frac{180-16\sqrt{155}}{-520}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-180)+16\sqrt{155}}{2*-260}=\frac{180+16\sqrt{155}}{-520}
$