Y=9x-7/5x-6

Solution for Y=9x-7/5x-6 equation:

=9Y-7/5Y-6

We move all terms to the left:

-(9Y-7/5Y-6)=0


Domain of the equation: 5Y-6)!=0

Y∈R


We get rid of parentheses

-9Y+7/5Y+6=0

We multiply all the terms by the denominator


-9Y*5Y+6*5Y+7=0

Wy multiply elements

-45Y^2+30Y+7=0

a = -45; b = 30; c = +7;
Δ = b2-4ac
Δ = 302-4·(-45)·7
Δ = 2160
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{2160}=\sqrt{144*15}=\sqrt{144}*\sqrt{15}=12\sqrt{15}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-12\sqrt{15}}{2*-45}=\frac{-30-12\sqrt{15}}{-90}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+12\sqrt{15}}{2*-45}=\frac{-30+12\sqrt{15}}{-90}
$