6x^2+3x+2x=27

Solution for 6x^2+3x+2x=27 equation:

6x^2+3x+2x=27

We move all terms to the left:

6x^2+3x+2x-(27)=0

We add all the numbers together, and all the variables

6x^2+5x-27=0

a = 6; b = 5; c = -27;
Δ = b2-4ac
Δ = 52-4·6·(-27)
Δ = 673
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{-(5)-\sqrt{673}}{2*6}=\frac{-5-\sqrt{673}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{673}}{2*6}=\frac{-5+\sqrt{673}}{12}
$