0.25x(6x+1)=2.5x+0.25

Solution for 0.25x(6x+1)=2.5x+0.25 equation:

0.25x(6x+1)=2.5x+0.25

We move all terms to the left:

0.25x(6x+1)-(2.5x+0.25)=0

We multiply parentheses

0x^2+0x-(2.5x+0.25)=0

We get rid of parentheses

0x^2+0x-2.5x-0.25=0

We add all the numbers together, and all the variables

x^2-1.5x-0.25=0

a = 1; b = -1.5; c = -0.25;
Δ = b2-4ac
Δ = -1.52-4·1·(-0.25)
Δ = 3.25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1.5)-\sqrt{3.25}}{2*1}=\frac{1.5-\sqrt{3.25}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1.5)+\sqrt{3.25}}{2*1}=\frac{1.5+\sqrt{3.25}}{2}
$