5x(x-2)+4(x-10)=0

Solution for 5x(x-2)+4(x-10)=0 equation:

5x(x-2)+4(x-10)=0

We multiply parentheses

5x^2-10x+4x-40=0

We add all the numbers together, and all the variables

5x^2-6x-40=0

a = 5; b = -6; c = -40;
Δ = b2-4ac
Δ = -62-4·5·(-40)
Δ = 836
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:

$\sqrt{\Delta}=\sqrt{836}=\sqrt{4*209}=\sqrt{4}*\sqrt{209}=2\sqrt{209}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{209}}{2*5}=\frac{6-2\sqrt{209}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{209}}{2*5}=\frac{6+2\sqrt{209}}{10}
$