Y=6x-1/7x+9

Solution for Y=6x-1/7x+9 equation:

=6Y-1/7Y+9

We move all terms to the left:

-(6Y-1/7Y+9)=0


Domain of the equation: 7Y+9)!=0

Y∈R


We get rid of parentheses

-6Y+1/7Y-9=0

We multiply all the terms by the denominator


-6Y*7Y-9*7Y+1=0

Wy multiply elements

-42Y^2-63Y+1=0

a = -42; b = -63; c = +1;
Δ = b2-4ac
Δ = -632-4·(-42)·1
Δ = 4137
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-63)-\sqrt{4137}}{2*-42}=\frac{63-\sqrt{4137}}{-84}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-63)+\sqrt{4137}}{2*-42}=\frac{63+\sqrt{4137}}{-84}
$