7w=(-5/6)

Solution for 7w=(-5/6) equation:

7w=(-5/6)

We move all terms to the left:

7w-((-5/6))=0

We multiply all the terms by the denominator


7w*6))-((-5=0

Wy multiply elements

42w^2-5=0

a = 42; b = 0; c = -5;
Δ = b2-4ac
Δ = 02-4·42·(-5)
Δ = 840
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:

$\sqrt{\Delta}=\sqrt{840}=\sqrt{4*210}=\sqrt{4}*\sqrt{210}=2\sqrt{210}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{210}}{2*42}=\frac{0-2\sqrt{210}}{84}
=-\frac{2\sqrt{210}}{84}
=-\frac{\sqrt{210}}{42}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{210}}{2*42}=\frac{0+2\sqrt{210}}{84}
=\frac{2\sqrt{210}}{84}
=\frac{\sqrt{210}}{42}
$