(x+3)(x+2)+9x=3(x2-5)-1

Solution for (x+3)(x+2)+9x=3(x2-5)-1 equation:

(x+3)(x+2)+9x=3(x2-5)-1

We move all terms to the left:

(x+3)(x+2)+9x-(3(x2-5)-1)=0

We add all the numbers together, and all the variables

-(3(+x^2-5)-1)+(x+3)(x+2)+9x=0

We add all the numbers together, and all the variables

-(3(+x^2-5)-1)+9x+(x+3)(x+2)=0

We multiply parentheses ..

-(3(+x^2-5)-1)+(+x^2+2x+3x+6)+9x=0


We calculate terms in parentheses: -(3(+x^2-5)-1), so:

3(+x^2-5)-1

We multiply parentheses

3x^2-15-1

We add all the numbers together, and all the variables

3x^2-16

Back to the equation:

-(3x^2-16)


We add all the numbers together, and all the variables

(+x^2+2x+3x+6)+9x-(3x^2-16)=0

We get rid of parentheses

x^2-3x^2+2x+3x+9x+6+16=0

We add all the numbers together, and all the variables

-2x^2+14x+22=0

a = -2; b = 14; c = +22;
Δ = b2-4ac
Δ = 142-4·(-2)·22
Δ = 372
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:

$\sqrt{\Delta}=\sqrt{372}=\sqrt{4*93}=\sqrt{4}*\sqrt{93}=2\sqrt{93}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-2\sqrt{93}}{2*-2}=\frac{-14-2\sqrt{93}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+2\sqrt{93}}{2*-2}=\frac{-14+2\sqrt{93}}{-4}
$