12x(5x+8)=34

Solution for 12x(5x+8)=34 equation:

12x(5x+8)=34

We move all terms to the left:

12x(5x+8)-(34)=0

We multiply parentheses

60x^2+96x-34=0

a = 60; b = 96; c = -34;
Δ = b2-4ac
Δ = 962-4·60·(-34)
Δ = 17376
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:

$\sqrt{\Delta}=\sqrt{17376}=\sqrt{16*1086}=\sqrt{16}*\sqrt{1086}=4\sqrt{1086}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(96)-4\sqrt{1086}}{2*60}=\frac{-96-4\sqrt{1086}}{120}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(96)+4\sqrt{1086}}{2*60}=\frac{-96+4\sqrt{1086}}{120}
$