2x(x+5x)-4=76

Solution for 2x(x+5x)-4=76 equation:

2x(x+5x)-4=76

We move all terms to the left:

2x(x+5x)-4-(76)=0

We add all the numbers together, and all the variables

2x(+6x)-4-76=0

We add all the numbers together, and all the variables

2x(+6x)-80=0

We multiply parentheses

12x^2-80=0

a = 12; b = 0; c = -80;
Δ = b2-4ac
Δ = 02-4·12·(-80)
Δ = 3840
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:

$\sqrt{\Delta}=\sqrt{3840}=\sqrt{256*15}=\sqrt{256}*\sqrt{15}=16\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-16\sqrt{15}}{2*12}=\frac{0-16\sqrt{15}}{24}
=-\frac{16\sqrt{15}}{24}
=-\frac{2\sqrt{15}}{3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+16\sqrt{15}}{2*12}=\frac{0+16\sqrt{15}}{24}
=\frac{16\sqrt{15}}{24}
=\frac{2\sqrt{15}}{3}
$