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

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

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

We move all terms to the left:

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

12x^2+8x-5=0

a = 12; b = 8; c = -5;
Δ = b2-4ac
Δ = 82-4·12·(-5)
Δ = 304
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:

$\sqrt{\Delta}=\sqrt{304}=\sqrt{16*19}=\sqrt{16}*\sqrt{19}=4\sqrt{19}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-4\sqrt{19}}{2*12}=\frac{-8-4\sqrt{19}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+4\sqrt{19}}{2*12}=\frac{-8+4\sqrt{19}}{24}
$