x=3/4x+5

Solution for x=3/4x+5 equation:

x=3/4x+5

We move all terms to the left:

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


Domain of the equation: 4x+5)!=0

x∈R


We get rid of parentheses

x-3/4x-5=0

We multiply all the terms by the denominator


x*4x-5*4x-3=0

Wy multiply elements

4x^2-20x-3=0

a = 4; b = -20; c = -3;
Δ = b2-4ac
Δ = -202-4·4·(-3)
Δ = 448
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:

$\sqrt{\Delta}=\sqrt{448}=\sqrt{64*7}=\sqrt{64}*\sqrt{7}=8\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-8\sqrt{7}}{2*4}=\frac{20-8\sqrt{7}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+8\sqrt{7}}{2*4}=\frac{20+8\sqrt{7}}{8}
$