2x^2+12x+9=143

Solution for 2x^2+12x+9=143 equation:

2x^2+12x+9=143

We move all terms to the left:

2x^2+12x+9-(143)=0

We add all the numbers together, and all the variables

2x^2+12x-134=0

a = 2; b = 12; c = -134;
Δ = b2-4ac
Δ = 122-4·2·(-134)
Δ = 1216
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:

$\sqrt{\Delta}=\sqrt{1216}=\sqrt{64*19}=\sqrt{64}*\sqrt{19}=8\sqrt{19}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-8\sqrt{19}}{2*2}=\frac{-12-8\sqrt{19}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+8\sqrt{19}}{2*2}=\frac{-12+8\sqrt{19}}{4}
$