9x+1=3x^2-15-x^2+x+6

Solution for 9x+1=3x^2-15-x^2+x+6 equation:

9x+1=3x^2-15-x^2+x+6

We move all terms to the left:

9x+1-(3x^2-15-x^2+x+6)=0

We get rid of parentheses

-3x^2+x^2-x+9x+15-6+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
$