5x(-3x+13)=-15x+65

Solution for 5x(-3x+13)=-15x+65 equation:

5x(-3x+13)=-15x+65

We move all terms to the left:

5x(-3x+13)-(-15x+65)=0

We multiply parentheses

-15x^2+65x-(-15x+65)=0

We get rid of parentheses

-15x^2+65x+15x-65=0

We add all the numbers together, and all the variables

-15x^2+80x-65=0

a = -15; b = 80; c = -65;
Δ = b2-4ac
Δ = 802-4·(-15)·(-65)
Δ = 2500
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2500}=50$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(80)-50}{2*-15}=\frac{-130}{-30}
=4+1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(80)+50}{2*-15}=\frac{-30}{-30}
=1
$