(2x^2+17x-9)/(2x-1)=0

Solution for (2x^2+17x-9)/(2x-1)=0 equation:

(2x^2+17x-9)/(2x-1)=0


Domain of the equation: (2x-1)!=0

We move all terms containing x to the left, all other terms to the right

2x!=1

x!=1/2

x!=1/2

x∈R


We multiply all the terms by the denominator


(2x^2+17x-9)=0

We get rid of parentheses

2x^2+17x-9=0

a = 2; b = 17; c = -9;
Δ = b2-4ac
Δ = 172-4·2·(-9)
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(17)-19}{2*2}=\frac{-36}{4}
=-9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+19}{2*2}=\frac{2}{4}
=1/2
$