(X)(2x+3)=52

Solution for (X)(2x+3)=52 equation:

(X)(2X+3)=52

We move all terms to the left:

(X)(2X+3)-(52)=0

We multiply parentheses

2X^2+3X-52=0

a = 2; b = 3; c = -52;
Δ = b2-4ac
Δ = 32-4·2·(-52)
Δ = 425
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:

$\sqrt{\Delta}=\sqrt{425}=\sqrt{25*17}=\sqrt{25}*\sqrt{17}=5\sqrt{17}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-5\sqrt{17}}{2*2}=\frac{-3-5\sqrt{17}}{4}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+5\sqrt{17}}{2*2}=\frac{-3+5\sqrt{17}}{4}
$