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(4/7)x=32
We move all terms to the left:
(4/7)x-(32)=0
Domain of the equation: 7)x!=0We add all the numbers together, and all the variables
x!=0/1
x!=0
x∈R
(+4/7)x-32=0
We multiply parentheses
4x^2-32=0
a = 4; b = 0; c = -32;
Δ = b2-4ac
Δ = 02-4·4·(-32)
Δ = 512
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{512}=\sqrt{256*2}=\sqrt{256}*\sqrt{2}=16\sqrt{2}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-16\sqrt{2}}{2*4}=\frac{0-16\sqrt{2}}{8} =-\frac{16\sqrt{2}}{8} =-2\sqrt{2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+16\sqrt{2}}{2*4}=\frac{0+16\sqrt{2}}{8} =\frac{16\sqrt{2}}{8} =2\sqrt{2} $
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