5x(3x-12)=10

Solution for 5x(3x-12)=10 equation:

5x(3x-12)=10

We move all terms to the left:

5x(3x-12)-(10)=0

We multiply parentheses

15x^2-60x-10=0

a = 15; b = -60; c = -10;
Δ = b2-4ac
Δ = -602-4·15·(-10)
Δ = 4200
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:

$\sqrt{\Delta}=\sqrt{4200}=\sqrt{100*42}=\sqrt{100}*\sqrt{42}=10\sqrt{42}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-60)-10\sqrt{42}}{2*15}=\frac{60-10\sqrt{42}}{30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+10\sqrt{42}}{2*15}=\frac{60+10\sqrt{42}}{30}
$