6+2(9x-12)8x=59-3x

Solution for 6+2(9x-12)8x=59-3x equation:

6+2(9x-12)8x=59-3x

We move all terms to the left:

6+2(9x-12)8x-(59-3x)=0

We add all the numbers together, and all the variables

2(9x-12)8x-(-3x+59)+6=0

We multiply parentheses

144x^2-192x-(-3x+59)+6=0

We get rid of parentheses

144x^2-192x+3x-59+6=0

We add all the numbers together, and all the variables

144x^2-189x-53=0

a = 144; b = -189; c = -53;
Δ = b2-4ac
Δ = -1892-4·144·(-53)
Δ = 66249
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:

$\sqrt{\Delta}=\sqrt{66249}=\sqrt{9*7361}=\sqrt{9}*\sqrt{7361}=3\sqrt{7361}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-189)-3\sqrt{7361}}{2*144}=\frac{189-3\sqrt{7361}}{288}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-189)+3\sqrt{7361}}{2*144}=\frac{189+3\sqrt{7361}}{288}
$