X(2x+3)=48

Solution for X(2x+3)=48 equation:

X(2X+3)=48

We move all terms to the left:

X(2X+3)-(48)=0

We multiply parentheses

2X^2+3X-48=0

a = 2; b = 3; c = -48;
Δ = b2-4ac
Δ = 32-4·2·(-48)
Δ = 393
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{-(3)-\sqrt{393}}{2*2}=\frac{-3-\sqrt{393}}{4}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{393}}{2*2}=\frac{-3+\sqrt{393}}{4}
$