5x(x-3)-10=0

Solution for 5x(x-3)-10=0 equation:

5x(x-3)-10=0

We multiply parentheses

5x^2-15x-10=0

a = 5; b = -15; c = -10;
Δ = b2-4ac
Δ = -152-4·5·(-10)
Δ = 425
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:

$\sqrt{\Delta}=\sqrt{425}=\sqrt{25*17}=\sqrt{25}*\sqrt{17}=5\sqrt{17}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-5\sqrt{17}}{2*5}=\frac{15-5\sqrt{17}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+5\sqrt{17}}{2*5}=\frac{15+5\sqrt{17}}{10}
$