X=4/5x+4=6

Solution for X=4/5x+4=6 equation:

X=4/5X+4=6

We move all terms to the left:

X-(4/5X+4)=0


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

X∈R


We get rid of parentheses

X-4/5X-4=0

We multiply all the terms by the denominator


X*5X-4*5X-4=0

Wy multiply elements

5X^2-20X-4=0

a = 5; b = -20; c = -4;
Δ = b2-4ac
Δ = -202-4·5·(-4)
Δ = 480
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:

$\sqrt{\Delta}=\sqrt{480}=\sqrt{16*30}=\sqrt{16}*\sqrt{30}=4\sqrt{30}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-4\sqrt{30}}{2*5}=\frac{20-4\sqrt{30}}{10}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+4\sqrt{30}}{2*5}=\frac{20+4\sqrt{30}}{10}
$