0=x^2+3x/2-14x

Solution for 0=x^2+3x/2-14x equation:

0=x^2+3x/2-14x

We move all terms to the left:

0-(x^2+3x/2-14x)=0


Domain of the equation: 2-14x)!=0

We move all terms containing x to the left, all other terms to the right

-14x)!=-2

x!=-2/1

x!=-2

x∈R


We add all the numbers together, and all the variables

-(x^2+3x/2-14x)=0

We get rid of parentheses

-x^2-3x/2+14x=0

We multiply all the terms by the denominator


-x^2*2-3x+14x*2=0

Wy multiply elements

-2x^2-3x+28x=0

We add all the numbers together, and all the variables

-2x^2+25x=0

a = -2; b = 25; c = 0;
Δ = b2-4ac
Δ = 252-4·(-2)·0
Δ = 625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{625}=25$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(25)-25}{2*-2}=\frac{-50}{-4}
=12+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(25)+25}{2*-2}=\frac{0}{-4}
=0
$