(2x-3)x/2=52

Solution for (2x-3)x/2=52 equation:

(2x-3)x/2=52

We move all terms to the left:

(2x-3)x/2-(52)=0

We multiply all the terms by the denominator


(2x-3)x-52*2=0

We add all the numbers together, and all the variables

(2x-3)x-104=0

We multiply parentheses

2x^2-3x-104=0

a = 2; b = -3; c = -104;
Δ = b2-4ac
Δ = -32-4·2·(-104)
Δ = 841
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{841}=29$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-29}{2*2}=\frac{-26}{4}
=-6+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+29}{2*2}=\frac{32}{4}
=8
$