Y=2x+7/4x-8

Solution for Y=2x+7/4x-8 equation:

=2Y+7/4Y-8

We move all terms to the left:

-(2Y+7/4Y-8)=0


Domain of the equation: 4Y-8)!=0

Y∈R


We get rid of parentheses

-2Y-7/4Y+8=0

We multiply all the terms by the denominator


-2Y*4Y+8*4Y-7=0

Wy multiply elements

-8Y^2+32Y-7=0

a = -8; b = 32; c = -7;
Δ = b2-4ac
Δ = 322-4·(-8)·(-7)
Δ = 800
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:

$\sqrt{\Delta}=\sqrt{800}=\sqrt{400*2}=\sqrt{400}*\sqrt{2}=20\sqrt{2}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(32)-20\sqrt{2}}{2*-8}=\frac{-32-20\sqrt{2}}{-16}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(32)+20\sqrt{2}}{2*-8}=\frac{-32+20\sqrt{2}}{-16}
$