-(1/2)-(7/3)x=-(9/4)

Solution for -(1/2)-(7/3)x=-(9/4) equation:

-(1/2)-(7/3)x=-(9/4)

We move all terms to the left:

-(1/2)-(7/3)x-(-(9/4))=0


Domain of the equation: 3)x!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

-(+7/3)x-(+1/2)-(-(+9/4))=0

We multiply parentheses

-7x^2-(+1/2)-(-(+9/4))=0

We get rid of parentheses

-7x^2-1/2-(-(+9/4))=0

We calculate fractions


-7x^2+()/()+()/()=0

We add all the numbers together, and all the variables

-7x^2+2=0

a = -7; b = 0; c = +2;
Δ = b2-4ac
Δ = 02-4·(-7)·2
Δ = 56
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:

$\sqrt{\Delta}=\sqrt{56}=\sqrt{4*14}=\sqrt{4}*\sqrt{14}=2\sqrt{14}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{14}}{2*-7}=\frac{0-2\sqrt{14}}{-14}
=-\frac{2\sqrt{14}}{-14}
=-\frac{\sqrt{14}}{-7}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{14}}{2*-7}=\frac{0+2\sqrt{14}}{-14}
=\frac{2\sqrt{14}}{-14}
=\frac{\sqrt{14}}{-7}
$