2x^2+6x+4=24^2

Solution for 2x^2+6x+4=24^2 equation:

2x^2+6x+4=24^2

We move all terms to the left:

2x^2+6x+4-(24^2)=0

We add all the numbers together, and all the variables

2x^2+6x-572=0

a = 2; b = 6; c = -572;
Δ = b2-4ac
Δ = 62-4·2·(-572)
Δ = 4612
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:

$\sqrt{\Delta}=\sqrt{4612}=\sqrt{4*1153}=\sqrt{4}*\sqrt{1153}=2\sqrt{1153}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{1153}}{2*2}=\frac{-6-2\sqrt{1153}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{1153}}{2*2}=\frac{-6+2\sqrt{1153}}{4}
$