(72x^2-118x+34)/(8x+2)=0

Solution for (72x^2-118x+34)/(8x+2)=0 equation:

(72x^2-118x+34)/(8x+2)=0


Domain of the equation: (8x+2)!=0

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

8x!=-2

x!=-2/8

x!=-1/4

x∈R


We multiply all the terms by the denominator


(72x^2-118x+34)=0

We get rid of parentheses

72x^2-118x+34=0

a = 72; b = -118; c = +34;
Δ = b2-4ac
Δ = -1182-4·72·34
Δ = 4132
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:

$\sqrt{\Delta}=\sqrt{4132}=\sqrt{4*1033}=\sqrt{4}*\sqrt{1033}=2\sqrt{1033}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-118)-2\sqrt{1033}}{2*72}=\frac{118-2\sqrt{1033}}{144}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-118)+2\sqrt{1033}}{2*72}=\frac{118+2\sqrt{1033}}{144}
$