102=4x(3x+2)

Solution for 102=4x(3x+2) equation:

102=4x(3x+2)

We move all terms to the left:

102-(4x(3x+2))=0


We calculate terms in parentheses: -(4x(3x+2)), so:

4x(3x+2)

We multiply parentheses

12x^2+8x

Back to the equation:

-(12x^2+8x)


We get rid of parentheses

-12x^2-8x+102=0

a = -12; b = -8; c = +102;
Δ = b2-4ac
Δ = -82-4·(-12)·102
Δ = 4960
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:

$\sqrt{\Delta}=\sqrt{4960}=\sqrt{16*310}=\sqrt{16}*\sqrt{310}=4\sqrt{310}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-4\sqrt{310}}{2*-12}=\frac{8-4\sqrt{310}}{-24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+4\sqrt{310}}{2*-12}=\frac{8+4\sqrt{310}}{-24}
$