(y^2-2)=7y/2

Solution for (y^2-2)=7y/2 equation:

(y^2-2)=7y/2

We move all terms to the left:

(y^2-2)-(7y/2)=0

We add all the numbers together, and all the variables

(y^2-2)-(+7y/2)=0

We get rid of parentheses

y^2-7y/2-2=0

We multiply all the terms by the denominator


y^2*2-7y-2*2=0

We add all the numbers together, and all the variables

y^2*2-7y-4=0

Wy multiply elements

2y^2-7y-4=0

a = 2; b = -7; c = -4;
Δ = b2-4ac
Δ = -72-4·2·(-4)
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-9}{2*2}=\frac{-2}{4}
=-1/2
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+9}{2*2}=\frac{16}{4}
=4
$