.5(6x-10)+(1/3)(6+9x)=0

Solution for .5(6x-10)+(1/3)(6+9x)=0 equation:

.5(6x-10)+(1/3)(6+9x)=0


Domain of the equation: 3)(6+9x)!=0

x∈R


We add all the numbers together, and all the variables

.5(6x-10)+(+1/3)(9x+6)=0

We multiply parentheses

3x+(+1/3)(9x+6)-5=0

We multiply parentheses ..

(+9x^2+1/3*6)+3x-5=0

We multiply all the terms by the denominator


(+9x^2+1+3x*3*6)-5*3*6)=0

We add all the numbers together, and all the variables

(+9x^2+1+3x*3*6)=0

We get rid of parentheses

9x^2+3x*3*6+1=0

Wy multiply elements

9x^2+54x*6+1=0

Wy multiply elements

9x^2+324x+1=0

a = 9; b = 324; c = +1;
Δ = b2-4ac
Δ = 3242-4·9·1
Δ = 104940
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{104940}=\sqrt{36*2915}=\sqrt{36}*\sqrt{2915}=6\sqrt{2915}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(324)-6\sqrt{2915}}{2*9}=\frac{-324-6\sqrt{2915}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(324)+6\sqrt{2915}}{2*9}=\frac{-324+6\sqrt{2915}}{18}
$