-(5/8)-(7/4)x=(5/2)

Solution for -(5/8)-(7/4)x=(5/2) equation:

-(5/8)-(7/4)x=(5/2)

We move all terms to the left:

-(5/8)-(7/4)x-((5/2))=0


Domain of the equation: 4)x!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

-(+7/4)x-(+5/8)-((+5/2))=0

We multiply parentheses

-7x^2-(+5/8)-((+5/2))=0

We get rid of parentheses

-7x^2-5/8-((+5/2))=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}
$