0.25x(4x-5)=0.75x+8

Solution for 0.25x(4x-5)=0.75x+8 equation:

0.25x(4x-5)=0.75x+8

We move all terms to the left:

0.25x(4x-5)-(0.75x+8)=0

We multiply parentheses

0x^2+0x-(0.75x+8)=0

We get rid of parentheses

0x^2+0x-0.75x-8=0

We add all the numbers together, and all the variables

x^2+0.25x-8=0

a = 1; b = 0.25; c = -8;
Δ = b2-4ac
Δ = 0.252-4·1·(-8)
Δ = 32.0625
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{-(0.25)-\sqrt{32.0625}}{2*1}=\frac{-0.25-\sqrt{32.0625}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0.25)+\sqrt{32.0625}}{2*1}=\frac{-0.25+\sqrt{32.0625}}{2}
$