5x(x+6)=10

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

5x(x+6)=10

We move all terms to the left:

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

We multiply parentheses

5x^2+30x-10=0

a = 5; b = 30; c = -10;
Δ = b2-4ac
Δ = 302-4·5·(-10)
Δ = 1100
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:

$\sqrt{\Delta}=\sqrt{1100}=\sqrt{100*11}=\sqrt{100}*\sqrt{11}=10\sqrt{11}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-10\sqrt{11}}{2*5}=\frac{-30-10\sqrt{11}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+10\sqrt{11}}{2*5}=\frac{-30+10\sqrt{11}}{10}
$