(3/4)x-1=7/5

Solution for (3/4)x-1=7/5 equation:

(3/4)x-1=7/5

We move all terms to the left:

(3/4)x-1-(7/5)=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

(+3/4)x-1-(+7/5)=0

We multiply parentheses

3x^2-1-(+7/5)=0

We get rid of parentheses

3x^2-1-7/5=0

We multiply all the terms by the denominator


3x^2*5-7-1*5=0

We add all the numbers together, and all the variables

3x^2*5-12=0

Wy multiply elements

15x^2-12=0

a = 15; b = 0; c = -12;
Δ = b2-4ac
Δ = 02-4·15·(-12)
Δ = 720
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:

$\sqrt{\Delta}=\sqrt{720}=\sqrt{144*5}=\sqrt{144}*\sqrt{5}=12\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{5}}{2*15}=\frac{0-12\sqrt{5}}{30}
=-\frac{12\sqrt{5}}{30}
=-\frac{2\sqrt{5}}{5}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{5}}{2*15}=\frac{0+12\sqrt{5}}{30}
=\frac{12\sqrt{5}}{30}
=\frac{2\sqrt{5}}{5}
$