(-7/4)w=-49

Solution for (-7/4)w=-49 equation:

(-7/4)w=-49

We move all terms to the left:

(-7/4)w-(-49)=0


Domain of the equation: 4)w!=0

w!=0/1

w!=0

w∈R


We add all the numbers together, and all the variables

(-7/4)w+49=0

We multiply parentheses

-7w^2+49=0

a = -7; b = 0; c = +49;
Δ = b2-4ac
Δ = 02-4·(-7)·49
Δ = 1372
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:

$\sqrt{\Delta}=\sqrt{1372}=\sqrt{196*7}=\sqrt{196}*\sqrt{7}=14\sqrt{7}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-14\sqrt{7}}{2*-7}=\frac{0-14\sqrt{7}}{-14}
=-\frac{14\sqrt{7}}{-14}
=-\frac{\sqrt{7}}{-1}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+14\sqrt{7}}{2*-7}=\frac{0+14\sqrt{7}}{-14}
=\frac{14\sqrt{7}}{-14}
=\frac{\sqrt{7}}{-1}
$