2x(x+6)+3=9+5x

Solution for 2x(x+6)+3=9+5x equation:

2x(x+6)+3=9+5x

We move all terms to the left:

2x(x+6)+3-(9+5x)=0

We add all the numbers together, and all the variables

2x(x+6)-(5x+9)+3=0

We multiply parentheses

2x^2+12x-(5x+9)+3=0

We get rid of parentheses

2x^2+12x-5x-9+3=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}
$