14x=30-4x^2

Solution for 14x=30-4x^2 equation:

14x=30-4x^2

We move all terms to the left:

14x-(30-4x^2)=0

We get rid of parentheses

4x^2+14x-30=0

a = 4; b = 14; c = -30;
Δ = b2-4ac
Δ = 142-4·4·(-30)
Δ = 676
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{676}=26$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-26}{2*4}=\frac{-40}{8}
=-5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+26}{2*4}=\frac{12}{8}
=1+1/2
$