5x(x-3)=12

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

5x(x-3)=12

We move all terms to the left:

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

We multiply parentheses

5x^2-15x-12=0

a = 5; b = -15; c = -12;
Δ = b2-4ac
Δ = -152-4·5·(-12)
Δ = 465
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-\sqrt{465}}{2*5}=\frac{15-\sqrt{465}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+\sqrt{465}}{2*5}=\frac{15+\sqrt{465}}{10}
$