(3)/(4)w-11=-(4)/(7)w

Solution for (3)/(4)w-11=-(4)/(7)w equation:

(3)/(4)w-11=-(4)/(7)w

We move all terms to the left:

(3)/(4)w-11-(-(4)/(7)w)=0


Domain of the equation: 4w!=0

w!=0/4

w!=0

w∈R



Domain of the equation: 7w)!=0

w!=0/1

w!=0

w∈R


We get rid of parentheses

3/4w+4/7w-11=0

We calculate fractions


21w/28w^2+16w/28w^2-11=0

We multiply all the terms by the denominator


21w+16w-11*28w^2=0

We add all the numbers together, and all the variables

37w-11*28w^2=0

Wy multiply elements

-308w^2+37w=0

a = -308; b = 37; c = 0;
Δ = b2-4ac
Δ = 372-4·(-308)·0
Δ = 1369
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1369}=37$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(37)-37}{2*-308}=\frac{-74}{-616}
=37/308
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(37)+37}{2*-308}=\frac{0}{-616}
=0
$