(-3/7)x=-4.5

Solution for (-3/7)x=-4.5 equation:

(-3/7)x=-4.5

We move all terms to the left:

(-3/7)x-(-4.5)=0


Domain of the equation: 7)x!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(-3/7)x+4.5=0

We multiply parentheses

-3x^2+4.5=0

a = -3; b = 0; c = +4.5;
Δ = b2-4ac
Δ = 02-4·(-3)·4.5
Δ = 54
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:

$\sqrt{\Delta}=\sqrt{54}=\sqrt{9*6}=\sqrt{9}*\sqrt{6}=3\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-3\sqrt{6}}{2*-3}=\frac{0-3\sqrt{6}}{-6}
=-\frac{3\sqrt{6}}{-6}
=-\frac{\sqrt{6}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+3\sqrt{6}}{2*-3}=\frac{0+3\sqrt{6}}{-6}
=\frac{3\sqrt{6}}{-6}
=\frac{\sqrt{6}}{-2}
$