7/6u=42u=

Solution for 7/6u=42u= equation:

7/6u=42u=

We move all terms to the left:

7/6u-(42u)=0


Domain of the equation: 6u!=0

u!=0/6

u!=0

u∈R


We add all the numbers together, and all the variables

-42u+7/6u=0

We multiply all the terms by the denominator


-42u*6u+7=0

Wy multiply elements

-252u^2+7=0

a = -252; b = 0; c = +7;
Δ = b2-4ac
Δ = 02-4·(-252)·7
Δ = 7056
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{7056}=84$
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-84}{2*-252}=\frac{-84}{-504}
=1/6
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+84}{2*-252}=\frac{84}{-504}
=-1/6
$