x^2-(34/25)x+(9/25)=0

Solution for x^2-(34/25)x+(9/25)=0 equation:

x^2-(34/25)x+(9/25)=0


Domain of the equation: 25)x!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

x^2-(+34/25)x+(+9/25)=0

We multiply parentheses

x^2-34x^2+(+9/25)=0

We get rid of parentheses

x^2-34x^2+9/25=0

We multiply all the terms by the denominator


x^2*25-34x^2*25+9=0

Wy multiply elements

25x^2-850x^2+9=0

We add all the numbers together, and all the variables

-825x^2+9=0

a = -825; b = 0; c = +9;
Δ = b2-4ac
Δ = 02-4·(-825)·9
Δ = 29700
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:

$\sqrt{\Delta}=\sqrt{29700}=\sqrt{900*33}=\sqrt{900}*\sqrt{33}=30\sqrt{33}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-30\sqrt{33}}{2*-825}=\frac{0-30\sqrt{33}}{-1650}
=-\frac{30\sqrt{33}}{-1650}
=-\frac{\sqrt{33}}{-55}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+30\sqrt{33}}{2*-825}=\frac{0+30\sqrt{33}}{-1650}
=\frac{30\sqrt{33}}{-1650}
=\frac{\sqrt{33}}{-55}
$