6x(3x+2)-5(6x-1)=3(x-8)-5(7x-6)+9x

Solution for 6x(3x+2)-5(6x-1)=3(x-8)-5(7x-6)+9x equation:

6x(3x+2)-5(6x-1)=3(x-8)-5(7x-6)+9x

We move all terms to the left:

6x(3x+2)-5(6x-1)-(3(x-8)-5(7x-6)+9x)=0

We multiply parentheses

18x^2+12x-30x-(3(x-8)-5(7x-6)+9x)+5=0


We calculate terms in parentheses: -(3(x-8)-5(7x-6)+9x), so:

3(x-8)-5(7x-6)+9x

We add all the numbers together, and all the variables

9x+3(x-8)-5(7x-6)

We multiply parentheses

9x+3x-35x-24+30

We add all the numbers together, and all the variables

-23x+6

Back to the equation:

-(-23x+6)


We add all the numbers together, and all the variables

18x^2-18x-(-23x+6)+5=0

We get rid of parentheses

18x^2-18x+23x-6+5=0

We add all the numbers together, and all the variables

18x^2+5x-1=0

a = 18; b = 5; c = -1;
Δ = b2-4ac
Δ = 52-4·18·(-1)
Δ = 97
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-\sqrt{97}}{2*18}=\frac{-5-\sqrt{97}}{36}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{97}}{2*18}=\frac{-5+\sqrt{97}}{36}
$