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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses ..

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


We calculate terms in parentheses: -(3(+x^2-5)-(+x^2+2x-3x-6)), so:

3(+x^2-5)-(+x^2+2x-3x-6)

We multiply parentheses

3x^2-(+x^2+2x-3x-6)-15

We get rid of parentheses

3x^2-x^2-2x+3x+6-15

We add all the numbers together, and all the variables

2x^2+x-9

Back to the equation:

-(2x^2+x-9)


We add all the numbers together, and all the variables

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

We get rid of parentheses

-2x^2+9x-x+9+1=0

We add all the numbers together, and all the variables

-2x^2+8x+10=0

a = -2; b = 8; c = +10;
Δ = b2-4ac
Δ = 82-4·(-2)·10
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-12}{2*-2}=\frac{-20}{-4}
=+5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+12}{2*-2}=\frac{4}{-4}
=-1
$