2x^2+14x+24/2=42

Solution for 2x^2+14x+24/2=42 equation:

2x^2+14x+24/2=42

We move all terms to the left:

2x^2+14x+24/2-(42)=0

determiningTheFunctionDomain
2x^2+14x-42+24/2=0

We add all the numbers together, and all the variables

2x^2+14x-30=0

a = 2; b = 14; c = -30;
Δ = b2-4ac
Δ = 142-4·2·(-30)
Δ = 436
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:

$\sqrt{\Delta}=\sqrt{436}=\sqrt{4*109}=\sqrt{4}*\sqrt{109}=2\sqrt{109}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-2\sqrt{109}}{2*2}=\frac{-14-2\sqrt{109}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+2\sqrt{109}}{2*2}=\frac{-14+2\sqrt{109}}{4}
$