6x2+34x+54=6

Solution for 6x2+34x+54=6 equation:

6x^2+34x+54=6

We move all terms to the left:

6x^2+34x+54-(6)=0

We add all the numbers together, and all the variables

6x^2+34x+48=0

a = 6; b = 34; c = +48;
Δ = b2-4ac
Δ = 342-4·6·48
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(34)-2}{2*6}=\frac{-36}{12}
=-3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(34)+2}{2*6}=\frac{-32}{12}
=-2+2/3
$