5x+6=2(x+6)x=

Solution for 5x+6=2(x+6)x= equation:

5x+6=2(x+6)x=

We move all terms to the left:

5x+6-(2(x+6)x)=0


We calculate terms in parentheses: -(2(x+6)x), so:

2(x+6)x

We multiply parentheses

2x^2+12x

Back to the equation:

-(2x^2+12x)


We get rid of parentheses

-2x^2+5x-12x+6=0

We add all the numbers together, and all the variables

-2x^2-7x+6=0

a = -2; b = -7; c = +6;
Δ = b2-4ac
Δ = -72-4·(-2)·6
Δ = 97
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-\sqrt{97}}{2*-2}=\frac{7-\sqrt{97}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{97}}{2*-2}=\frac{7+\sqrt{97}}{-4}
$