-2/3x+15(x=3)

Solution for -2/3x+15(x=3) equation:

-2/3x+15(x=3)

We move all terms to the left:

-2/3x+15(x-(3))=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We multiply parentheses

-2/3x+15x-45=0

We multiply all the terms by the denominator


15x*3x-45*3x-2=0

Wy multiply elements

45x^2-135x-2=0

a = 45; b = -135; c = -2;
Δ = b2-4ac
Δ = -1352-4·45·(-2)
Δ = 18585
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:

$\sqrt{\Delta}=\sqrt{18585}=\sqrt{9*2065}=\sqrt{9}*\sqrt{2065}=3\sqrt{2065}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-135)-3\sqrt{2065}}{2*45}=\frac{135-3\sqrt{2065}}{90}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-135)+3\sqrt{2065}}{2*45}=\frac{135+3\sqrt{2065}}{90}
$