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(5/2)x=16-7x

We move all terms to the left:

(5/2)x-(16-7x)=0

Domain of the equation: 2)x!=0We add all the numbers together, and all the variables

x!=0/1

x!=0

x∈R

(+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 = b^{2}-4ac

Δ = 7^{2}-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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