5x(4x+2)=10

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

5x(4x+2)=10

We move all terms to the left:

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

We multiply parentheses

20x^2+10x-10=0

a = 20; b = 10; c = -10;
Δ = b2-4ac
Δ = 102-4·20·(-10)
Δ = 900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{900}=30$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-30}{2*20}=\frac{-40}{40}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+30}{2*20}=\frac{20}{40}
=1/2
$