x(2x-5)=46

Solution for x(2x-5)=46 equation:

x(2x-5)=46

We move all terms to the left:

x(2x-5)-(46)=0

We multiply parentheses

2x^2-5x-46=0

a = 2; b = -5; c = -46;
Δ = b2-4ac
Δ = -52-4·2·(-46)
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{-(-5)-\sqrt{393}}{2*2}=\frac{5-\sqrt{393}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{393}}{2*2}=\frac{5+\sqrt{393}}{4}
$