12x(2x+5)=10

Solution for 12x(2x+5)=10 equation:

12x(2x+5)=10

We move all terms to the left:

12x(2x+5)-(10)=0

We multiply parentheses

24x^2+60x-10=0

a = 24; b = 60; c = -10;
Δ = b2-4ac
Δ = 602-4·24·(-10)
Δ = 4560
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:

$\sqrt{\Delta}=\sqrt{4560}=\sqrt{16*285}=\sqrt{16}*\sqrt{285}=4\sqrt{285}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(60)-4\sqrt{285}}{2*24}=\frac{-60-4\sqrt{285}}{48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(60)+4\sqrt{285}}{2*24}=\frac{-60+4\sqrt{285}}{48}
$