25x^2=30x-5

Solution for 25x^2=30x-5 equation:

25x^2=30x-5

We move all terms to the left:

25x^2-(30x-5)=0

We get rid of parentheses

25x^2-30x+5=0

a = 25; b = -30; c = +5;
Δ = b2-4ac
Δ = -302-4·25·5
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-20}{2*25}=\frac{10}{50}
=1/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+20}{2*25}=\frac{50}{50}
=1
$