2w+7=1/2w+10

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

2w+7=1/2w+10

We move all terms to the left:

2w+7-(1/2w+10)=0


Domain of the equation: 2w+10)!=0

w∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


2w*2w-10*2w+7*2w-1=0

Wy multiply elements

4w^2-20w+14w-1=0

We add all the numbers together, and all the variables

4w^2-6w-1=0

a = 4; b = -6; c = -1;
Δ = b2-4ac
Δ = -62-4·4·(-1)
Δ = 52
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:

$\sqrt{\Delta}=\sqrt{52}=\sqrt{4*13}=\sqrt{4}*\sqrt{13}=2\sqrt{13}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{13}}{2*4}=\frac{6-2\sqrt{13}}{8}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{13}}{2*4}=\frac{6+2\sqrt{13}}{8}
$