(4/9)x+32=77

Solution for (4/9)x+32=77 equation:

(4/9)x+32=77

We move all terms to the left:

(4/9)x+32-(77)=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

(+4/9)x+32-77=0

We add all the numbers together, and all the variables

(+4/9)x-45=0

We multiply parentheses

4x^2-45=0

a = 4; b = 0; c = -45;
Δ = b2-4ac
Δ = 02-4·4·(-45)
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*4}=\frac{0-12\sqrt{5}}{8}
=-\frac{12\sqrt{5}}{8}
=-\frac{3\sqrt{5}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{5}}{2*4}=\frac{0+12\sqrt{5}}{8}
=\frac{12\sqrt{5}}{8}
=\frac{3\sqrt{5}}{2}
$