X-15=2/5x+6

Solution for X-15=2/5x+6 equation:

X-15=2/5X+6

We move all terms to the left:

X-15-(2/5X+6)=0


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

X∈R


We get rid of parentheses

X-2/5X-6-15=0

We multiply all the terms by the denominator


X*5X-6*5X-15*5X-2=0

Wy multiply elements

5X^2-30X-75X-2=0

We add all the numbers together, and all the variables

5X^2-105X-2=0

a = 5; b = -105; c = -2;
Δ = b2-4ac
Δ = -1052-4·5·(-2)
Δ = 11065
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-105)-\sqrt{11065}}{2*5}=\frac{105-\sqrt{11065}}{10}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-105)+\sqrt{11065}}{2*5}=\frac{105+\sqrt{11065}}{10}
$