4(1/2x+3)=3x+12-x2

Solution for 4(1/2x+3)=3x+12-x2 equation:

4(1/2x+3)=3x+12-x2

We move all terms to the left:

4(1/2x+3)-(3x+12-x2)=0


Domain of the equation: 2x+3)!=0

x∈R


We add all the numbers together, and all the variables

-(+3x-1x^2+12)+4(1/2x+3)=0

We multiply parentheses

-(+3x-1x^2+12)+4x+12=0

We get rid of parentheses

1x^2-3x+4x-12+12=0

We add all the numbers together, and all the variables

x^2+x=0

a = 1; b = 1; c = 0;
Δ = b2-4ac
Δ = 12-4·1·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-1}{2*1}=\frac{-2}{2}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+1}{2*1}=\frac{0}{2}
=0
$