52=(2x-5)x

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

52=(2x-5)x

We move all terms to the left:

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


We calculate terms in parentheses: -((2x-5)x), so:

(2x-5)x

We multiply parentheses

2x^2-5x

Back to the equation:

-(2x^2-5x)


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