3/4x-5=4/5*

Solution for 3/4x-5=4/5* equation:

3/4x-5=4/5*

We move all terms to the left:

3/4x-5-(4/5*)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

3/4x-5-(+4/5*)=0

We get rid of parentheses

3/4x-5-4/5*=0

We calculate fractions


()/20x^2+(-16x)/20x^2-5=0

We multiply all the terms by the denominator


(-16x)-5*20x^2+()=0

We add all the numbers together, and all the variables

(-16x)-5*20x^2=0

Wy multiply elements

-100x^2+(-16x)=0

We get rid of parentheses

-100x^2-16x=0

a = -100; b = -16; c = 0;
Δ = b2-4ac
Δ = -162-4·(-100)·0
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-16}{2*-100}=\frac{0}{-200}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+16}{2*-100}=\frac{32}{-200}
=-4/25
$