Y=4x+5/2x-7

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

=4Y+5/2Y-7

We move all terms to the left:

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


Domain of the equation: 2Y-7)!=0

Y∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

-8Y^2+14Y-5=0

a = -8; b = 14; c = -5;
Δ = b2-4ac
Δ = 142-4·(-8)·(-5)
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-6}{2*-8}=\frac{-20}{-16}
=1+1/4
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+6}{2*-8}=\frac{-8}{-16}
=1/2
$