5x(2x+6)=48

Solution for 5x(2x+6)=48 equation:

5x(2x+6)=48

We move all terms to the left:

5x(2x+6)-(48)=0

We multiply parentheses

10x^2+30x-48=0

a = 10; b = 30; c = -48;
Δ = b2-4ac
Δ = 302-4·10·(-48)
Δ = 2820
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:

$\sqrt{\Delta}=\sqrt{2820}=\sqrt{4*705}=\sqrt{4}*\sqrt{705}=2\sqrt{705}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-2\sqrt{705}}{2*10}=\frac{-30-2\sqrt{705}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+2\sqrt{705}}{2*10}=\frac{-30+2\sqrt{705}}{20}
$