x^2+(4/9)x+(4900/9)=1225

Solution for x^2+(4/9)x+(4900/9)=1225 equation:

x^2+(4/9)x+(4900/9)=1225

We move all terms to the left:

x^2+(4/9)x+(4900/9)-(1225)=0


Domain of the equation: 9)x!=0

x!=0/1

x!=0

x∈R


determiningTheFunctionDomain
x^2+(4/9)x-1225+(4900/9)=0

We add all the numbers together, and all the variables

x^2+(+4/9)x-1225+(+4900/9)=0

We multiply parentheses

x^2+4x^2-1225+(+4900/9)=0

We get rid of parentheses

x^2+4x^2-1225+4900/9=0

We multiply all the terms by the denominator


x^2*9+4x^2*9+4900-1225*9=0

We add all the numbers together, and all the variables

x^2*9+4x^2*9-6125=0

Wy multiply elements

9x^2+36x^2-6125=0

We add all the numbers together, and all the variables

45x^2-6125=0

a = 45; b = 0; c = -6125;
Δ = b2-4ac
Δ = 02-4·45·(-6125)
Δ = 1102500
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1102500}=1050$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-1050}{2*45}=\frac{-1050}{90}
=-11+2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+1050}{2*45}=\frac{1050}{90}
=11+2/3
$