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

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

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

We move all terms to the left:

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

We multiply parentheses

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


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

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

We multiply parentheses

-315x^2+3x+270x-24

We add all the numbers together, and all the variables

-315x^2+273x-24

Back to the equation:

-(-315x^2+273x-24)


We add all the numbers together, and all the variables

-(-315x^2+273x-24)-12x+17=0

We get rid of parentheses

315x^2-273x-12x+24+17=0

We add all the numbers together, and all the variables

315x^2-285x+41=0

a = 315; b = -285; c = +41;
Δ = b2-4ac
Δ = -2852-4·315·41
Δ = 29565
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:

$\sqrt{\Delta}=\sqrt{29565}=\sqrt{81*365}=\sqrt{81}*\sqrt{365}=9\sqrt{365}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-285)-9\sqrt{365}}{2*315}=\frac{285-9\sqrt{365}}{630}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-285)+9\sqrt{365}}{2*315}=\frac{285+9\sqrt{365}}{630}
$