5x(x-2)-6=24

Solution for 5x(x-2)-6=24 equation:

5x(x-2)-6=24

We move all terms to the left:

5x(x-2)-6-(24)=0

We add all the numbers together, and all the variables

5x(x-2)-30=0

We multiply parentheses

5x^2-10x-30=0

a = 5; b = -10; c = -30;
Δ = b2-4ac
Δ = -102-4·5·(-30)
Δ = 700
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:

$\sqrt{\Delta}=\sqrt{700}=\sqrt{100*7}=\sqrt{100}*\sqrt{7}=10\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-10\sqrt{7}}{2*5}=\frac{10-10\sqrt{7}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+10\sqrt{7}}{2*5}=\frac{10+10\sqrt{7}}{10}
$