5x(x+1)-10-2=0

Solution for 5x(x+1)-10-2=0 equation:

5x(x+1)-10-2=0

We add all the numbers together, and all the variables

5x(x+1)-12=0

We multiply parentheses

5x^2+5x-12=0

a = 5; b = 5; c = -12;
Δ = b2-4ac
Δ = 52-4·5·(-12)
Δ = 265
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{-(5)-\sqrt{265}}{2*5}=\frac{-5-\sqrt{265}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{265}}{2*5}=\frac{-5+\sqrt{265}}{10}
$