(-10/9)x=-8

Solution for (-10/9)x=-8 equation:

(-10/9)x=-8

We move all terms to the left:

(-10/9)x-(-8)=0


Domain of the equation: 9)x!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(-10/9)x+8=0

We multiply parentheses

-10x^2+8=0

a = -10; b = 0; c = +8;
Δ = b2-4ac
Δ = 02-4·(-10)·8
Δ = 320
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:

$\sqrt{\Delta}=\sqrt{320}=\sqrt{64*5}=\sqrt{64}*\sqrt{5}=8\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{5}}{2*-10}=\frac{0-8\sqrt{5}}{-20}
=-\frac{8\sqrt{5}}{-20}
=-\frac{2\sqrt{5}}{-5}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{5}}{2*-10}=\frac{0+8\sqrt{5}}{-20}
=\frac{8\sqrt{5}}{-20}
=\frac{2\sqrt{5}}{-5}
$