5(x-19)-3x(x-12)=13

Solution for 5(x-19)-3x(x-12)=13 equation:

5(x-19)-3x(x-12)=13

We move all terms to the left:

5(x-19)-3x(x-12)-(13)=0

We multiply parentheses

-3x^2+5x+36x-95-13=0

We add all the numbers together, and all the variables

-3x^2+41x-108=0

a = -3; b = 41; c = -108;
Δ = b2-4ac
Δ = 412-4·(-3)·(-108)
Δ = 385
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{-(41)-\sqrt{385}}{2*-3}=\frac{-41-\sqrt{385}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(41)+\sqrt{385}}{2*-3}=\frac{-41+\sqrt{385}}{-6}
$