Y=-1/2x+23x-4Y=12

Solution for Y=-1/2x+23x-4Y=12 equation:

=-1/2Y+23Y-4=12

We move all terms to the left:

-(-1/2Y+23Y-4)=0


Domain of the equation: 2Y+23Y-4)!=0

Y∈R


We add all the numbers together, and all the variables

-(23Y-1/2Y-4)=0

We get rid of parentheses

-23Y+1/2Y+4=0

We multiply all the terms by the denominator


-23Y*2Y+4*2Y+1=0

Wy multiply elements

-46Y^2+8Y+1=0

a = -46; b = 8; c = +1;
Δ = b2-4ac
Δ = 82-4·(-46)·1
Δ = 248
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:

$\sqrt{\Delta}=\sqrt{248}=\sqrt{4*62}=\sqrt{4}*\sqrt{62}=2\sqrt{62}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-2\sqrt{62}}{2*-46}=\frac{-8-2\sqrt{62}}{-92}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+2\sqrt{62}}{2*-46}=\frac{-8+2\sqrt{62}}{-92}
$