6x2+12x+6=148

Solution for 6x2+12x+6=148 equation:

6x^2+12x+6=148

We move all terms to the left:

6x^2+12x+6-(148)=0

We add all the numbers together, and all the variables

6x^2+12x-142=0

a = 6; b = 12; c = -142;
Δ = b2-4ac
Δ = 122-4·6·(-142)
Δ = 3552
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:

$\sqrt{\Delta}=\sqrt{3552}=\sqrt{16*222}=\sqrt{16}*\sqrt{222}=4\sqrt{222}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-4\sqrt{222}}{2*6}=\frac{-12-4\sqrt{222}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+4\sqrt{222}}{2*6}=\frac{-12+4\sqrt{222}}{12}
$