Y=x-5/x+4=8x+7

Solution for Y=x-5/x+4=8x+7 equation:

=Y-5/Y+4=8Y+7

We move all terms to the left:

-(Y-5/Y+4)=0


Domain of the equation: Y+4)!=0

Y∈R


We get rid of parentheses

-Y+5/Y-4=0

We multiply all the terms by the denominator


-Y*Y-4*Y+5=0

We add all the numbers together, and all the variables

-4Y-Y*Y+5=0

Wy multiply elements

-1Y^2-4Y+5=0

a = -1; b = -4; c = +5;
Δ = b2-4ac
Δ = -42-4·(-1)·5
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-6}{2*-1}=\frac{-2}{-2}
=1
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+6}{2*-1}=\frac{10}{-2}
=-5
$