(x(x-3))/(2)=152

Solution for (x(x-3))/(2)=152 equation:

(x(x-3))/(2)=152

We move all terms to the left:

(x(x-3))/(2)-(152)=0

We multiply all the terms by the denominator


(x(x-3))-152*2=0


We calculate terms in parentheses: +(x(x-3)), so:

x(x-3)

We multiply parentheses

x^2-3x

Back to the equation:

+(x^2-3x)


We add all the numbers together, and all the variables

(x^2-3x)-304=0

We get rid of parentheses

x^2-3x-304=0

a = 1; b = -3; c = -304;
Δ = b2-4ac
Δ = -32-4·1·(-304)
Δ = 1225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1225}=35$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-35}{2*1}=\frac{-32}{2}
=-16
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+35}{2*1}=\frac{38}{2}
=19
$