4x^2=-6+14x

Solution for 4x^2=-6+14x equation:

4x^2=-6+14x

We move all terms to the left:

4x^2-(-6+14x)=0

We add all the numbers together, and all the variables

4x^2-(14x-6)=0

We get rid of parentheses

4x^2-14x+6=0

a = 4; b = -14; c = +6;
Δ = b2-4ac
Δ = -142-4·4·6
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-10}{2*4}=\frac{4}{8}
=1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+10}{2*4}=\frac{24}{8}
=3
$