(9/5)x=12/5

Solution for (9/5)x=12/5 equation:

(9/5)x=12/5

We move all terms to the left:

(9/5)x-(12/5)=0


Domain of the equation: 5)x!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(+9/5)x-(+12/5)=0

We multiply parentheses

9x^2-(+12/5)=0

We get rid of parentheses

9x^2-12/5=0

We multiply all the terms by the denominator


9x^2*5-12=0

Wy multiply elements

45x^2-12=0

a = 45; b = 0; c = -12;
Δ = b2-4ac
Δ = 02-4·45·(-12)
Δ = 2160
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:

$\sqrt{\Delta}=\sqrt{2160}=\sqrt{144*15}=\sqrt{144}*\sqrt{15}=12\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{15}}{2*45}=\frac{0-12\sqrt{15}}{90}
=-\frac{12\sqrt{15}}{90}
=-\frac{2\sqrt{15}}{15}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{15}}{2*45}=\frac{0+12\sqrt{15}}{90}
=\frac{12\sqrt{15}}{90}
=\frac{2\sqrt{15}}{15}
$