3x^2+2x+3=56

Solution for 3x^2+2x+3=56 equation:

3x^2+2x+3=56

We move all terms to the left:

3x^2+2x+3-(56)=0

We add all the numbers together, and all the variables

3x^2+2x-53=0

a = 3; b = 2; c = -53;
Δ = b2-4ac
Δ = 22-4·3·(-53)
Δ = 640
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:

$\sqrt{\Delta}=\sqrt{640}=\sqrt{64*10}=\sqrt{64}*\sqrt{10}=8\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-8\sqrt{10}}{2*3}=\frac{-2-8\sqrt{10}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+8\sqrt{10}}{2*3}=\frac{-2+8\sqrt{10}}{6}
$