5x2=10x-25/9

Solution for 5x2=10x-25/9 equation:

5x^2=10x-25/9

We move all terms to the left:

5x^2-(10x-25/9)=0

We add all the numbers together, and all the variables

5x^2-(+10x-25/9)=0

We get rid of parentheses

5x^2-10x+25/9=0

We multiply all the terms by the denominator


5x^2*9-10x*9+25=0

Wy multiply elements

45x^2-90x+25=0

a = 45; b = -90; c = +25;
Δ = b2-4ac
Δ = -902-4·45·25
Δ = 3600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3600}=60$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-90)-60}{2*45}=\frac{30}{90}
=1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-90)+60}{2*45}=\frac{150}{90}
=1+2/3
$