4x2-6x=14

Solution for 4x2-6x=14 equation:

4x^2-6x=14

We move all terms to the left:

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

a = 4; b = -6; c = -14;
Δ = b2-4ac
Δ = -62-4·4·(-14)
Δ = 260
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:

$\sqrt{\Delta}=\sqrt{260}=\sqrt{4*65}=\sqrt{4}*\sqrt{65}=2\sqrt{65}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{65}}{2*4}=\frac{6-2\sqrt{65}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{65}}{2*4}=\frac{6+2\sqrt{65}}{8}
$