7x-(3/2)*(4x-9)=6.5

Solution for 7x-(3/2)*(4x-9)=6.5 equation:

7x-(3/2)(4x-9)=6.5

We move all terms to the left:

7x-(3/2)(4x-9)-(6.5)=0


Domain of the equation: 2)(4x-9)!=0

x∈R


We add all the numbers together, and all the variables

7x-(+3/2)(4x-9)-(6.5)=0

We add all the numbers together, and all the variables

7x-(+3/2)(4x-9)-6.5=0

We multiply parentheses ..

-(+12x^2+3/2*-9)+7x-6.5=0

We multiply all the terms by the denominator


-(+12x^2+3+7x*2*-9)-(6.5)*2*-9)=0

We add all the numbers together, and all the variables

-(+12x^2+3+7x*2*-9)=0

We get rid of parentheses

-12x^2-7x*2*-3+9=0

We add all the numbers together, and all the variables

-12x^2-7x*2*+6=0

Wy multiply elements

-12x^2-14x^2+6=0

We add all the numbers together, and all the variables

-26x^2+6=0

a = -26; b = 0; c = +6;
Δ = b2-4ac
Δ = 02-4·(-26)·6
Δ = 624
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:

$\sqrt{\Delta}=\sqrt{624}=\sqrt{16*39}=\sqrt{16}*\sqrt{39}=4\sqrt{39}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{39}}{2*-26}=\frac{0-4\sqrt{39}}{-52}
=-\frac{4\sqrt{39}}{-52}
=-\frac{\sqrt{39}}{-13}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{39}}{2*-26}=\frac{0+4\sqrt{39}}{-52}
=\frac{4\sqrt{39}}{-52}
=\frac{\sqrt{39}}{-13}
$