4x^2=30+14x

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

4x^2=30+14x

We move all terms to the left:

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

We add all the numbers together, and all the variables

4x^2-(14x+30)=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{-12}{8}
=-1+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+26}{2*4}=\frac{40}{8}
=5
$