X=2/5x+6

Solution for X=2/5x+6 equation:

X=2/5X+6

We move all terms to the left:

X-(2/5X+6)=0


Domain of the equation: 5X+6)!=0

X∈R


We get rid of parentheses

X-2/5X-6=0

We multiply all the terms by the denominator


X*5X-6*5X-2=0

Wy multiply elements

5X^2-30X-2=0

a = 5; b = -30; c = -2;
Δ = b2-4ac
Δ = -302-4·5·(-2)
Δ = 940
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:

$\sqrt{\Delta}=\sqrt{940}=\sqrt{4*235}=\sqrt{4}*\sqrt{235}=2\sqrt{235}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-2\sqrt{235}}{2*5}=\frac{30-2\sqrt{235}}{10}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+2\sqrt{235}}{2*5}=\frac{30+2\sqrt{235}}{10}
$