(3/2)(3x-2)-10x-3=0

Solution for (3/2)(3x-2)-10x-3=0 equation:

(3/2)(3x-2)-10x-3=0


Domain of the equation: 2)(3x-2)!=0

x∈R


We add all the numbers together, and all the variables

(+3/2)(3x-2)-10x-3=0

We add all the numbers together, and all the variables

-10x+(+3/2)(3x-2)-3=0

We multiply parentheses ..

(+9x^2+3/2*-2)-10x-3=0

We multiply all the terms by the denominator


(+9x^2+3-10x*2*-2)-3*2*-2)=0

We add all the numbers together, and all the variables

(+9x^2+3-10x*2*-2)=0

We get rid of parentheses

9x^2-10x*2*+3-2=0

We add all the numbers together, and all the variables

9x^2-10x*2*+1=0

Wy multiply elements

9x^2-20x^2+1=0

We add all the numbers together, and all the variables

-11x^2+1=0

a = -11; b = 0; c = +1;
Δ = b2-4ac
Δ = 02-4·(-11)·1
Δ = 44
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:

$\sqrt{\Delta}=\sqrt{44}=\sqrt{4*11}=\sqrt{4}*\sqrt{11}=2\sqrt{11}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{11}}{2*-11}=\frac{0-2\sqrt{11}}{-22}
=-\frac{2\sqrt{11}}{-22}
=-\frac{\sqrt{11}}{-11}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{11}}{2*-11}=\frac{0+2\sqrt{11}}{-22}
=\frac{2\sqrt{11}}{-22}
=\frac{\sqrt{11}}{-11}
$