x^2=5x/2+1.5

Solution for x^2=5x/2+1.5 equation:

x^2=5x/2+1.5

We move all terms to the left:

x^2-(5x/2+1.5)=0

We get rid of parentheses

x^2-5x/2-1.5=0

We multiply all the terms by the denominator


x^2*2-5x-(1.5)*2=0

We add all the numbers together, and all the variables

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

Wy multiply elements

2x^2-5x-3=0

a = 2; b = -5; c = -3;
Δ = b2-4ac
Δ = -52-4·2·(-3)
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-7}{2*2}=\frac{-2}{4}
=-1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+7}{2*2}=\frac{12}{4}
=3
$