5x+14+3x=x^2

Solution for 5x+14+3x=x^2 equation:

5x+14+3x=x^2

We move all terms to the left:

5x+14+3x-(x^2)=0

determiningTheFunctionDomain
-x^2+5x+3x+14=0

We add all the numbers together, and all the variables

-1x^2+8x+14=0

a = -1; b = 8; c = +14;
Δ = b2-4ac
Δ = 82-4·(-1)·14
Δ = 120
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:

$\sqrt{\Delta}=\sqrt{120}=\sqrt{4*30}=\sqrt{4}*\sqrt{30}=2\sqrt{30}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-2\sqrt{30}}{2*-1}=\frac{-8-2\sqrt{30}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+2\sqrt{30}}{2*-1}=\frac{-8+2\sqrt{30}}{-2}
$