Y=5x+2/7x+8

Solution for Y=5x+2/7x+8 equation:

=5Y+2/7Y+8

We move all terms to the left:

-(5Y+2/7Y+8)=0


Domain of the equation: 7Y+8)!=0

Y∈R


We get rid of parentheses

-5Y-2/7Y-8=0

We multiply all the terms by the denominator


-5Y*7Y-8*7Y-2=0

Wy multiply elements

-35Y^2-56Y-2=0

a = -35; b = -56; c = -2;
Δ = b2-4ac
Δ = -562-4·(-35)·(-2)
Δ = 2856
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:

$\sqrt{\Delta}=\sqrt{2856}=\sqrt{4*714}=\sqrt{4}*\sqrt{714}=2\sqrt{714}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-56)-2\sqrt{714}}{2*-35}=\frac{56-2\sqrt{714}}{-70}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-56)+2\sqrt{714}}{2*-35}=\frac{56+2\sqrt{714}}{-70}
$