5(3x+9)-2x=15x-2)x-5)

Solution for 5(3x+9)-2x=15x-2)x-5) equation:

5(3x+9)-2x=15x-2)x-5)

We move all terms to the left:

5(3x+9)-2x-(15x-2)x-5))=0

We add all the numbers together, and all the variables

-2x+5(3x+9)-(15x-2)x=0

We multiply parentheses

-15x^2-2x+15x+2x+45=0

We add all the numbers together, and all the variables

-15x^2+15x+45=0

a = -15; b = 15; c = +45;
Δ = b2-4ac
Δ = 152-4·(-15)·45
Δ = 2925
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:

$\sqrt{\Delta}=\sqrt{2925}=\sqrt{225*13}=\sqrt{225}*\sqrt{13}=15\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-15\sqrt{13}}{2*-15}=\frac{-15-15\sqrt{13}}{-30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+15\sqrt{13}}{2*-15}=\frac{-15+15\sqrt{13}}{-30}
$