9u+2/7u=4

Solution for 9u+2/7u=4 equation:

9u+2/7u=4

We move all terms to the left:

9u+2/7u-(4)=0


Domain of the equation: 7u!=0

u!=0/7

u!=0

u∈R


We multiply all the terms by the denominator


9u*7u-4*7u+2=0

Wy multiply elements

63u^2-28u+2=0

a = 63; b = -28; c = +2;
Δ = b2-4ac
Δ = -282-4·63·2
Δ = 280
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{280}=\sqrt{4*70}=\sqrt{4}*\sqrt{70}=2\sqrt{70}$
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-28)-2\sqrt{70}}{2*63}=\frac{28-2\sqrt{70}}{126}
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-28)+2\sqrt{70}}{2*63}=\frac{28+2\sqrt{70}}{126}
$