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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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


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

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

We multiply parentheses

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

We get rid of parentheses

3x^2-x-2-15

We add all the numbers together, and all the variables

3x^2-1x-17

Back to the equation:

-(3x^2-1x-17)


We add all the numbers together, and all the variables

9x-(3x^2-1x-17)+1=0

We get rid of parentheses

-3x^2+9x+1x+17+1=0

We add all the numbers together, and all the variables

-3x^2+10x+18=0

a = -3; b = 10; c = +18;
Δ = b2-4ac
Δ = 102-4·(-3)·18
Δ = 316
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:

$\sqrt{\Delta}=\sqrt{316}=\sqrt{4*79}=\sqrt{4}*\sqrt{79}=2\sqrt{79}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{79}}{2*-3}=\frac{-10-2\sqrt{79}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{79}}{2*-3}=\frac{-10+2\sqrt{79}}{-6}
$