9/4w+1=7/10w+3

Solution for 9/4w+1=7/10w+3 equation:

9/4w+1=7/10w+3

We move all terms to the left:

9/4w+1-(7/10w+3)=0


Domain of the equation: 4w!=0

w!=0/4

w!=0

w∈R



Domain of the equation: 10w+3)!=0

w∈R


We get rid of parentheses

9/4w-7/10w-3+1=0

We calculate fractions


90w/40w^2+(-28w)/40w^2-3+1=0

We add all the numbers together, and all the variables

90w/40w^2+(-28w)/40w^2-2=0

We multiply all the terms by the denominator


90w+(-28w)-2*40w^2=0

Wy multiply elements

-80w^2+90w+(-28w)=0

We get rid of parentheses

-80w^2+90w-28w=0

We add all the numbers together, and all the variables

-80w^2+62w=0

a = -80; b = 62; c = 0;
Δ = b2-4ac
Δ = 622-4·(-80)·0
Δ = 3844
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3844}=62$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(62)-62}{2*-80}=\frac{-124}{-160}
=31/40
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(62)+62}{2*-80}=\frac{0}{-160}
=0
$