9x(-6+2x)4=18x+0.5

Solution for 9x(-6+2x)4=18x+0.5 equation:

9x(-6+2x)4=18x+0.5

We move all terms to the left:

9x(-6+2x)4-(18x+0.5)=0

We add all the numbers together, and all the variables

9x(2x-6)4-(18x+0.5)=0

We multiply parentheses

72x^2-216x-(18x+0.5)=0

We get rid of parentheses

72x^2-216x-18x-0.5=0

We add all the numbers together, and all the variables

72x^2-234x-0.5=0

a = 72; b = -234; c = -0.5;
Δ = b2-4ac
Δ = -2342-4·72·(-0.5)
Δ = 54900
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:

$\sqrt{\Delta}=\sqrt{54900}=\sqrt{900*61}=\sqrt{900}*\sqrt{61}=30\sqrt{61}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-234)-30\sqrt{61}}{2*72}=\frac{234-30\sqrt{61}}{144}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-234)+30\sqrt{61}}{2*72}=\frac{234+30\sqrt{61}}{144}
$