Y=7x-1/3x+8

Solution for Y=7x-1/3x+8 equation:

=7Y-1/3Y+8

We move all terms to the left:

-(7Y-1/3Y+8)=0


Domain of the equation: 3Y+8)!=0

Y∈R


We get rid of parentheses

-7Y+1/3Y-8=0

We multiply all the terms by the denominator


-7Y*3Y-8*3Y+1=0

Wy multiply elements

-21Y^2-24Y+1=0

a = -21; b = -24; c = +1;
Δ = b2-4ac
Δ = -242-4·(-21)·1
Δ = 660
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:

$\sqrt{\Delta}=\sqrt{660}=\sqrt{4*165}=\sqrt{4}*\sqrt{165}=2\sqrt{165}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-2\sqrt{165}}{2*-21}=\frac{24-2\sqrt{165}}{-42}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+2\sqrt{165}}{2*-21}=\frac{24+2\sqrt{165}}{-42}
$