3x^2+44x-7=-3

Solution for 3x^2+44x-7=-3 equation:

3x^2+44x-7=-3

We move all terms to the left:

3x^2+44x-7-(-3)=0

We add all the numbers together, and all the variables

3x^2+44x-4=0

a = 3; b = 44; c = -4;
Δ = b2-4ac
Δ = 442-4·3·(-4)
Δ = 1984
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:

$\sqrt{\Delta}=\sqrt{1984}=\sqrt{64*31}=\sqrt{64}*\sqrt{31}=8\sqrt{31}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(44)-8\sqrt{31}}{2*3}=\frac{-44-8\sqrt{31}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(44)+8\sqrt{31}}{2*3}=\frac{-44+8\sqrt{31}}{6}
$