(7/2)x-1=2x+9

Solution for (7/2)x-1=2x+9 equation:

(7/2)x-1=2x+9

We move all terms to the left:

(7/2)x-1-(2x+9)=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

(+7/2)x-(2x+9)-1=0

We multiply parentheses

7x^2-(2x+9)-1=0

We get rid of parentheses

7x^2-2x-9-1=0

We add all the numbers together, and all the variables

7x^2-2x-10=0

a = 7; b = -2; c = -10;
Δ = b2-4ac
Δ = -22-4·7·(-10)
Δ = 284
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:

$\sqrt{\Delta}=\sqrt{284}=\sqrt{4*71}=\sqrt{4}*\sqrt{71}=2\sqrt{71}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{71}}{2*7}=\frac{2-2\sqrt{71}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{71}}{2*7}=\frac{2+2\sqrt{71}}{14}
$