1/4x+3=2x-5

Solution for 1/4x+3=2x-5 equation:

1/4x+3=2x-5

We move all terms to the left:

1/4x+3-(2x-5)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We get rid of parentheses

1/4x-2x+5+3=0

We multiply all the terms by the denominator


-2x*4x+5*4x+3*4x+1=0

Wy multiply elements

-8x^2+20x+12x+1=0

We add all the numbers together, and all the variables

-8x^2+32x+1=0

a = -8; b = 32; c = +1;
Δ = b2-4ac
Δ = 322-4·(-8)·1
Δ = 1056
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:

$\sqrt{\Delta}=\sqrt{1056}=\sqrt{16*66}=\sqrt{16}*\sqrt{66}=4\sqrt{66}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(32)-4\sqrt{66}}{2*-8}=\frac{-32-4\sqrt{66}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(32)+4\sqrt{66}}{2*-8}=\frac{-32+4\sqrt{66}}{-16}
$