12x-4=12x(x-2)-17

Solution for 12x-4=12x(x-2)-17 equation:

12x-4=12x(x-2)-17

We move all terms to the left:

12x-4-(12x(x-2)-17)=0


We calculate terms in parentheses: -(12x(x-2)-17), so:

12x(x-2)-17

We multiply parentheses

12x^2-24x-17

Back to the equation:

-(12x^2-24x-17)


We get rid of parentheses

-12x^2+12x+24x+17-4=0

We add all the numbers together, and all the variables

-12x^2+36x+13=0

a = -12; b = 36; c = +13;
Δ = b2-4ac
Δ = 362-4·(-12)·13
Δ = 1920
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:

$\sqrt{\Delta}=\sqrt{1920}=\sqrt{64*30}=\sqrt{64}*\sqrt{30}=8\sqrt{30}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(36)-8\sqrt{30}}{2*-12}=\frac{-36-8\sqrt{30}}{-24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+8\sqrt{30}}{2*-12}=\frac{-36+8\sqrt{30}}{-24}
$