5x(x+3)=48

Solution for 5x(x+3)=48 equation:

5x(x+3)=48

We move all terms to the left:

5x(x+3)-(48)=0

We multiply parentheses

5x^2+15x-48=0

a = 5; b = 15; c = -48;
Δ = b2-4ac
Δ = 152-4·5·(-48)
Δ = 1185
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-\sqrt{1185}}{2*5}=\frac{-15-\sqrt{1185}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+\sqrt{1185}}{2*5}=\frac{-15+\sqrt{1185}}{10}
$