x(0,5x+1,5)=0,25(4x+1,5)

Solution for x(0,5x+1,5)=0,25(4x+1,5) equation:

x(0.5x+1.5)=0.25(4x+1.5)

We move all terms to the left:

x(0.5x+1.5)-(0.25(4x+1.5))=0

We multiply parentheses

0x^2+1.5x-(0.25(4x+1.5))=0


We calculate terms in parentheses: -(0.25(4x+1.5)), so:

0.25(4x+1.5)

We multiply parentheses

x+0.375

Back to the equation:

-(x+0.375)


We add all the numbers together, and all the variables

x^2+1.5x-(x+0.375)=0

We get rid of parentheses

x^2+1.5x-x-0.375=0

We add all the numbers together, and all the variables

x^2+0.5x-0.375=0

a = 1; b = 0.5; c = -0.375;
Δ = b2-4ac
Δ = 0.52-4·1·(-0.375)
Δ = 1.75
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{-(0.5)-\sqrt{1.75}}{2*1}=\frac{-0.5-\sqrt{1.75}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0.5)+\sqrt{1.75}}{2*1}=\frac{-0.5+\sqrt{1.75}}{2}
$