1/2(6x+3)-8x(3x-9)=13/2

Solution for 1/2(6x+3)-8x(3x-9)=13/2 equation:

1/2(6x+3)-8x(3x-9)=13/2

We move all terms to the left:

1/2(6x+3)-8x(3x-9)-(13/2)=0


Domain of the equation: 2(6x+3)!=0

x∈R


We add all the numbers together, and all the variables

1/2(6x+3)-8x(3x-9)-(+13/2)=0

We multiply parentheses

-24x^2+1/2(6x+3)+72x-(+13/2)=0

We get rid of parentheses

-24x^2+1/2(6x+3)+72x-13/2=0

We calculate fractions


-24x^2+72x=0

a = -24; b = 72; c = 0;
Δ = b2-4ac
Δ = 722-4·(-24)·0
Δ = 5184
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5184}=72$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(72)-72}{2*-24}=\frac{-144}{-48}
=+3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(72)+72}{2*-24}=\frac{0}{-48}
=0
$