(x^2)/4=3x+14

Solution for (x^2)/4=3x+14 equation:

(x^2)/4=3x+14

We move all terms to the left:

(x^2)/4-(3x+14)=0

We get rid of parentheses

x^2/4-3x-14=0

We multiply all the terms by the denominator


x^2-3x*4-14*4=0

We add all the numbers together, and all the variables

x^2-3x*4-56=0

Wy multiply elements

x^2-12x-56=0

a = 1; b = -12; c = -56;
Δ = b2-4ac
Δ = -122-4·1·(-56)
Δ = 368
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:

$\sqrt{\Delta}=\sqrt{368}=\sqrt{16*23}=\sqrt{16}*\sqrt{23}=4\sqrt{23}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-4\sqrt{23}}{2*1}=\frac{12-4\sqrt{23}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+4\sqrt{23}}{2*1}=\frac{12+4\sqrt{23}}{2}
$