3.149+3x(5+x)=45-12+x

Solution for 3.149+3x(5+x)=45-12+x equation:

3.149+3x(5+x)=45-12+x

We move all terms to the left:

3.149+3x(5+x)-(45-12+x)=0

We add all the numbers together, and all the variables

3x(x+5)-(x+33)+3.149=0

We multiply parentheses

3x^2+15x-(x+33)+3.149=0

We get rid of parentheses

3x^2+15x-x-33+3.149=0

We add all the numbers together, and all the variables

3x^2+14x-29.851=0

a = 3; b = 14; c = -29.851;
Δ = b2-4ac
Δ = 142-4·3·(-29.851)
Δ = 554.212
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-\sqrt{554.212}}{2*3}=\frac{-14-\sqrt{554.212}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+\sqrt{554.212}}{2*3}=\frac{-14+\sqrt{554.212}}{6}
$