x(2x-5)=3/2

Solution for x(2x-5)=3/2 equation:

x(2x-5)=3/2

We move all terms to the left:

x(2x-5)-(3/2)=0

We add all the numbers together, and all the variables

x(2x-5)-(+3/2)=0

We multiply parentheses

2x^2-5x-(+3/2)=0

We get rid of parentheses

2x^2-5x-3/2=0

We multiply all the terms by the denominator


2x^2*2-5x*2-3=0

Wy multiply elements

4x^2-10x-3=0

a = 4; b = -10; c = -3;
Δ = b2-4ac
Δ = -102-4·4·(-3)
Δ = 148
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{148}=\sqrt{4*37}=\sqrt{4}*\sqrt{37}=2\sqrt{37}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{37}}{2*4}=\frac{10-2\sqrt{37}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{37}}{2*4}=\frac{10+2\sqrt{37}}{8}
$