4(3+2x)x=76

Solution for 4(3+2x)x=76 equation:

4(3+2x)x=76

We move all terms to the left:

4(3+2x)x-(76)=0

We add all the numbers together, and all the variables

4(2x+3)x-76=0

We multiply parentheses

8x^2+12x-76=0

a = 8; b = 12; c = -76;
Δ = b2-4ac
Δ = 122-4·8·(-76)
Δ = 2576
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:

$\sqrt{\Delta}=\sqrt{2576}=\sqrt{16*161}=\sqrt{16}*\sqrt{161}=4\sqrt{161}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-4\sqrt{161}}{2*8}=\frac{-12-4\sqrt{161}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+4\sqrt{161}}{2*8}=\frac{-12+4\sqrt{161}}{16}
$