4(x-2)-x(4x-13)=-5

Solution for 4(x-2)-x(4x-13)=-5 equation:

4(x-2)-x(4x-13)=-5

We move all terms to the left:

4(x-2)-x(4x-13)-(-5)=0

We add all the numbers together, and all the variables

4(x-2)-x(4x-13)+5=0

We multiply parentheses

-4x^2+4x+13x-8+5=0

We add all the numbers together, and all the variables

-4x^2+17x-3=0

a = -4; b = 17; c = -3;
Δ = b2-4ac
Δ = 172-4·(-4)·(-3)
Δ = 241
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{-(17)-\sqrt{241}}{2*-4}=\frac{-17-\sqrt{241}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+\sqrt{241}}{2*-4}=\frac{-17+\sqrt{241}}{-8}
$