3x^2-14x-4=10x

Solution for 3x^2-14x-4=10x equation:

3x^2-14x-4=10x

We move all terms to the left:

3x^2-14x-4-(10x)=0

We add all the numbers together, and all the variables

3x^2-24x-4=0

a = 3; b = -24; c = -4;
Δ = b2-4ac
Δ = -242-4·3·(-4)
Δ = 624
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:

$\sqrt{\Delta}=\sqrt{624}=\sqrt{16*39}=\sqrt{16}*\sqrt{39}=4\sqrt{39}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-4\sqrt{39}}{2*3}=\frac{24-4\sqrt{39}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+4\sqrt{39}}{2*3}=\frac{24+4\sqrt{39}}{6}
$