Y=1/2x+x-12

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

=1/2Y+Y-12

We move all terms to the left:

-(1/2Y+Y-12)=0


Domain of the equation: 2Y+Y-12)!=0

Y∈R


We add all the numbers together, and all the variables

-(Y+1/2Y-12)=0

We get rid of parentheses

-Y-1/2Y+12=0

We multiply all the terms by the denominator


-Y*2Y+12*2Y-1=0

Wy multiply elements

-2Y^2+24Y-1=0

a = -2; b = 24; c = -1;
Δ = b2-4ac
Δ = 242-4·(-2)·(-1)
Δ = 568
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:

$\sqrt{\Delta}=\sqrt{568}=\sqrt{4*142}=\sqrt{4}*\sqrt{142}=2\sqrt{142}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-2\sqrt{142}}{2*-2}=\frac{-24-2\sqrt{142}}{-4}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+2\sqrt{142}}{2*-2}=\frac{-24+2\sqrt{142}}{-4}
$