Y=4x-7/2x+5

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

=4Y-7/2Y+5

We move all terms to the left:

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


Domain of the equation: 2Y+5)!=0

Y∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

-8Y^2-10Y+7=0

a = -8; b = -10; c = +7;
Δ = b2-4ac
Δ = -102-4·(-8)·7
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-18}{2*-8}=\frac{-8}{-16}
=1/2
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+18}{2*-8}=\frac{28}{-16}
=-1+3/4
$