Y=2y-5/4y+7

Solution for Y=2y-5/4y+7 equation:

=2Y-5/4Y+7

We move all terms to the left:

-(2Y-5/4Y+7)=0


Domain of the equation: 4Y+7)!=0

Y∈R


We get rid of parentheses

-2Y+5/4Y-7=0

We multiply all the terms by the denominator


-2Y*4Y-7*4Y+5=0

Wy multiply elements

-8Y^2-28Y+5=0

a = -8; b = -28; c = +5;
Δ = b2-4ac
Δ = -282-4·(-8)·5
Δ = 944
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:

$\sqrt{\Delta}=\sqrt{944}=\sqrt{16*59}=\sqrt{16}*\sqrt{59}=4\sqrt{59}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-28)-4\sqrt{59}}{2*-8}=\frac{28-4\sqrt{59}}{-16}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-28)+4\sqrt{59}}{2*-8}=\frac{28+4\sqrt{59}}{-16}
$