(5/2)x=16-7x

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Solution for (5/2)x=16-7x equation:



(5/2)x=16-7x
We move all terms to the left:
(5/2)x-(16-7x)=0
Domain of the equation: 2)x!=0
x!=0/1
x!=0
x∈R
We add all the numbers together, and all the variables
(+5/2)x-(-7x+16)=0
We multiply parentheses
5x^2-(-7x+16)=0
We get rid of parentheses
5x^2+7x-16=0
a = 5; b = 7; c = -16;
Δ = b2-4ac
Δ = 72-4·5·(-16)
Δ = 369
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:
$\sqrt{\Delta}=\sqrt{369}=\sqrt{9*41}=\sqrt{9}*\sqrt{41}=3\sqrt{41}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-3\sqrt{41}}{2*5}=\frac{-7-3\sqrt{41}}{10} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+3\sqrt{41}}{2*5}=\frac{-7+3\sqrt{41}}{10} $

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