6x+2x+9=3+4x2

Solution for 6x+2x+9=3+4x2 equation:

6x+2x+9=3+4x^2

We move all terms to the left:

6x+2x+9-(3+4x^2)=0

We add all the numbers together, and all the variables

-(3+4x^2)+8x+9=0

We get rid of parentheses

-4x^2+8x-3+9=0

We add all the numbers together, and all the variables

-4x^2+8x+6=0

a = -4; b = 8; c = +6;
Δ = b2-4ac
Δ = 82-4·(-4)·6
Δ = 160
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:

$\sqrt{\Delta}=\sqrt{160}=\sqrt{16*10}=\sqrt{16}*\sqrt{10}=4\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-4\sqrt{10}}{2*-4}=\frac{-8-4\sqrt{10}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+4\sqrt{10}}{2*-4}=\frac{-8+4\sqrt{10}}{-8}
$