x=-23/4x-8=10

Solution for x=-23/4x-8=10 equation:

x=-23/4x-8=10

We move all terms to the left:

x-(-23/4x-8)=0


Domain of the equation: 4x-8)!=0

x∈R


We get rid of parentheses

x+23/4x+8=0

We multiply all the terms by the denominator


x*4x+8*4x+23=0

Wy multiply elements

4x^2+32x+23=0

a = 4; b = 32; c = +23;
Δ = b2-4ac
Δ = 322-4·4·23
Δ = 656
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:

$\sqrt{\Delta}=\sqrt{656}=\sqrt{16*41}=\sqrt{16}*\sqrt{41}=4\sqrt{41}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(32)-4\sqrt{41}}{2*4}=\frac{-32-4\sqrt{41}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(32)+4\sqrt{41}}{2*4}=\frac{-32+4\sqrt{41}}{8}
$