6x-2x(x-6)=4(x+1)+9

Solution for 6x-2x(x-6)=4(x+1)+9 equation:

6x-2x(x-6)=4(x+1)+9

We move all terms to the left:

6x-2x(x-6)-(4(x+1)+9)=0

We multiply parentheses

-2x^2+6x+12x-(4(x+1)+9)=0


We calculate terms in parentheses: -(4(x+1)+9), so:

4(x+1)+9

We multiply parentheses

4x+4+9

We add all the numbers together, and all the variables

4x+13

Back to the equation:

-(4x+13)


We add all the numbers together, and all the variables

-2x^2+18x-(4x+13)=0

We get rid of parentheses

-2x^2+18x-4x-13=0

We add all the numbers together, and all the variables

-2x^2+14x-13=0

a = -2; b = 14; c = -13;
Δ = b2-4ac
Δ = 142-4·(-2)·(-13)
Δ = 92
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:

$\sqrt{\Delta}=\sqrt{92}=\sqrt{4*23}=\sqrt{4}*\sqrt{23}=2\sqrt{23}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-2\sqrt{23}}{2*-2}=\frac{-14-2\sqrt{23}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+2\sqrt{23}}{2*-2}=\frac{-14+2\sqrt{23}}{-4}
$