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(1/4)x-7=38
We move all terms to the left:
(1/4)x-7-(38)=0
Domain of the equation: 4)x!=0We add all the numbers together, and all the variables
x!=0/1
x!=0
x∈R
(+1/4)x-7-38=0
We add all the numbers together, and all the variables
(+1/4)x-45=0
We multiply parentheses
x^2-45=0
a = 1; b = 0; c = -45;
Δ = b2-4ac
Δ = 02-4·1·(-45)
Δ = 180
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{180}=\sqrt{36*5}=\sqrt{36}*\sqrt{5}=6\sqrt{5}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{5}}{2*1}=\frac{0-6\sqrt{5}}{2} =-\frac{6\sqrt{5}}{2} =-3\sqrt{5} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{5}}{2*1}=\frac{0+6\sqrt{5}}{2} =\frac{6\sqrt{5}}{2} =3\sqrt{5} $
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