25x^2+5x=5/16

Solution for 25x^2+5x=5/16 equation:

25x^2+5x=5/16

We move all terms to the left:

25x^2+5x-(5/16)=0

We add all the numbers together, and all the variables

25x^2+5x-(+5/16)=0

We get rid of parentheses

25x^2+5x-5/16=0

We multiply all the terms by the denominator


25x^2*16+5x*16-5=0

Wy multiply elements

400x^2+80x-5=0

a = 400; b = 80; c = -5;
Δ = b2-4ac
Δ = 802-4·400·(-5)
Δ = 14400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{14400}=120$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(80)-120}{2*400}=\frac{-200}{800}
=-1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(80)+120}{2*400}=\frac{40}{800}
=1/20
$