5x(6+4x)=10

Solution for 5x(6+4x)=10 equation:

5x(6+4x)=10

We move all terms to the left:

5x(6+4x)-(10)=0

We add all the numbers together, and all the variables

5x(4x+6)-10=0

We multiply parentheses

20x^2+30x-10=0

a = 20; b = 30; c = -10;
Δ = b2-4ac
Δ = 302-4·20·(-10)
Δ = 1700
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:

$\sqrt{\Delta}=\sqrt{1700}=\sqrt{100*17}=\sqrt{100}*\sqrt{17}=10\sqrt{17}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-10\sqrt{17}}{2*20}=\frac{-30-10\sqrt{17}}{40}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+10\sqrt{17}}{2*20}=\frac{-30+10\sqrt{17}}{40}
$