2.75x+(-3)=-1/4x+21

Solution for 2.75x+(-3)=-1/4x+21 equation:

2.75x+(-3)=-1/4x+21

We move all terms to the left:

2.75x+(-3)-(-1/4x+21)=0


Domain of the equation: 4x+21)!=0

x∈R


We add all the numbers together, and all the variables

2.75x-(-1/4x+21)-3=0

We get rid of parentheses

2.75x+1/4x-21-3=0

We multiply all the terms by the denominator


(2.75x)*4x-21*4x-3*4x+1=0

We add all the numbers together, and all the variables

(+2.75x)*4x-21*4x-3*4x+1=0

We multiply parentheses

8x^2-21*4x-3*4x+1=0

Wy multiply elements

8x^2-84x-12x+1=0

We add all the numbers together, and all the variables

8x^2-96x+1=0

a = 8; b = -96; c = +1;
Δ = b2-4ac
Δ = -962-4·8·1
Δ = 9184
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{9184}=\sqrt{16*574}=\sqrt{16}*\sqrt{574}=4\sqrt{574}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-96)-4\sqrt{574}}{2*8}=\frac{96-4\sqrt{574}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-96)+4\sqrt{574}}{2*8}=\frac{96+4\sqrt{574}}{16}
$