X2+4x+3=47123

Solution for X2+4x+3=47123 equation:

X2+4X+3=47123

We move all terms to the left:

X2+4X+3-(47123)=0

We add all the numbers together, and all the variables

X^2+4X-47120=0

a = 1; b = 4; c = -47120;
Δ = b2-4ac
Δ = 42-4·1·(-47120)
Δ = 188496
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:

$\sqrt{\Delta}=\sqrt{188496}=\sqrt{144*1309}=\sqrt{144}*\sqrt{1309}=12\sqrt{1309}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-12\sqrt{1309}}{2*1}=\frac{-4-12\sqrt{1309}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+12\sqrt{1309}}{2*1}=\frac{-4+12\sqrt{1309}}{2}
$