6x+9=2(x+4);x=1/4

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

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

We move all terms to the left:

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


We calculate terms in parentheses: -(2(x+4)x), so:

2(x+4)x

We multiply parentheses

2x^2+8x

Back to the equation:

-(2x^2+8x)


We get rid of parentheses

-2x^2+6x-8x+9=0

We add all the numbers together, and all the variables

-2x^2-2x+9=0

a = -2; b = -2; c = +9;
Δ = b2-4ac
Δ = -22-4·(-2)·9
Δ = 76
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:

$\sqrt{\Delta}=\sqrt{76}=\sqrt{4*19}=\sqrt{4}*\sqrt{19}=2\sqrt{19}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{19}}{2*-2}=\frac{2-2\sqrt{19}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{19}}{2*-2}=\frac{2+2\sqrt{19}}{-4}
$