5(0.25p-1)=5/4p-1.4

Solution for 5(0.25p-1)=5/4p-1.4 equation:

5(0.25p-1)=5/4p-1.4

We move all terms to the left:

5(0.25p-1)-(5/4p-1.4)=0


Domain of the equation: 4p-1.4)!=0

p∈R


We multiply parentheses

0p-(5/4p-1.4)-5=0

We get rid of parentheses

0p-5/4p+1.4-5=0

We multiply all the terms by the denominator


0p*4p+(1.4)*4p-5*4p-5=0

We multiply parentheses

0p*4p+5.6p-5*4p-5=0

Wy multiply elements

0p^2+5.6p-20p-5=0

We add all the numbers together, and all the variables

p^2-14.4p-5=0

a = 1; b = -14.4; c = -5;
Δ = b2-4ac
Δ = -14.42-4·1·(-5)
Δ = 227.36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14.4)-\sqrt{227.36}}{2*1}=\frac{14.4-\sqrt{227.36}}{2}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14.4)+\sqrt{227.36}}{2*1}=\frac{14.4+\sqrt{227.36}}{2}
$