0.25(x-3)=3x-11/4x-3

Solution for 0.25(x-3)=3x-11/4x-3 equation:

0.25(x-3)=3x-11/4x-3

We move all terms to the left:

0.25(x-3)-(3x-11/4x-3)=0


Domain of the equation: 4x-3)!=0

x∈R


We multiply parentheses

0.25x-(3x-11/4x-3)-0.75=0

We get rid of parentheses

0.25x-3x+11/4x+3-0.75=0

We multiply all the terms by the denominator


(0.25x)*4x-3x*4x+3*4x-(0.75)*4x+11=0

We add all the numbers together, and all the variables

(+0.25x)*4x-3x*4x+3*4x-(0.75)*4x+11=0

We multiply parentheses

0x^2-3x*4x+3*4x-3x+11=0

Wy multiply elements

0x^2-12x^2+12x-3x+11=0

We add all the numbers together, and all the variables

-11x^2+9x+11=0

a = -11; b = 9; c = +11;
Δ = b2-4ac
Δ = 92-4·(-11)·11
Δ = 565
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{-(9)-\sqrt{565}}{2*-11}=\frac{-9-\sqrt{565}}{-22}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+\sqrt{565}}{2*-11}=\frac{-9+\sqrt{565}}{-22}
$