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

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

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

We move all terms to the left:

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


Domain of the equation: 2x+5)!=0

x∈R


We add all the numbers together, and all the variables

4x-(-5/2x+6)-4=0

We get rid of parentheses

4x+5/2x-6-4=0

We multiply all the terms by the denominator


4x*2x-6*2x-4*2x+5=0

Wy multiply elements

8x^2-12x-8x+5=0

We add all the numbers together, and all the variables

8x^2-20x+5=0

a = 8; b = -20; c = +5;
Δ = b2-4ac
Δ = -202-4·8·5
Δ = 240
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:

$\sqrt{\Delta}=\sqrt{240}=\sqrt{16*15}=\sqrt{16}*\sqrt{15}=4\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-4\sqrt{15}}{2*8}=\frac{20-4\sqrt{15}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+4\sqrt{15}}{2*8}=\frac{20+4\sqrt{15}}{16}
$