x(2x-5)=52

Solution for x(2x-5)=52 equation:

x(2x-5)=52

We move all terms to the left:

x(2x-5)-(52)=0

We multiply parentheses

2x^2-5x-52=0

a = 2; b = -5; c = -52;
Δ = b2-4ac
Δ = -52-4·2·(-52)
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-21}{2*2}=\frac{-16}{4}
=-4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+21}{2*2}=\frac{26}{4}
=6+1/2
$