X(2x+5)=23

Solution for X(2x+5)=23 equation:

X(2X+5)=23

We move all terms to the left:

X(2X+5)-(23)=0

We multiply parentheses

2X^2+5X-23=0

a = 2; b = 5; c = -23;
Δ = b2-4ac
Δ = 52-4·2·(-23)
Δ = 209
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{-(5)-\sqrt{209}}{2*2}=\frac{-5-\sqrt{209}}{4}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{209}}{2*2}=\frac{-5+\sqrt{209}}{4}
$