4=-5x+8/2x+6

Solution for 4=-5x+8/2x+6 equation:

4=-5x+8/2x+6

We move all terms to the left:

4-(-5x+8/2x+6)=0


Domain of the equation: 2x+6)!=0

x∈R


We get rid of parentheses

5x-8/2x-6+4=0

We multiply all the terms by the denominator


5x*2x-6*2x+4*2x-8=0

Wy multiply elements

10x^2-12x+8x-8=0

We add all the numbers together, and all the variables

10x^2-4x-8=0

a = 10; b = -4; c = -8;
Δ = b2-4ac
Δ = -42-4·10·(-8)
Δ = 336
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:

$\sqrt{\Delta}=\sqrt{336}=\sqrt{16*21}=\sqrt{16}*\sqrt{21}=4\sqrt{21}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4\sqrt{21}}{2*10}=\frac{4-4\sqrt{21}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4\sqrt{21}}{2*10}=\frac{4+4\sqrt{21}}{20}
$