(5/2)x=16-7x

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}
$