5x(x-1)+3(x-4)=-1

Solution for 5x(x-1)+3(x-4)=-1 equation:

5x(x-1)+3(x-4)=-1

We move all terms to the left:

5x(x-1)+3(x-4)-(-1)=0

We add all the numbers together, and all the variables

5x(x-1)+3(x-4)+1=0

We multiply parentheses

5x^2-5x+3x-12+1=0

We add all the numbers together, and all the variables

5x^2-2x-11=0

a = 5; b = -2; c = -11;
Δ = b2-4ac
Δ = -22-4·5·(-11)
Δ = 224
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:

$\sqrt{\Delta}=\sqrt{224}=\sqrt{16*14}=\sqrt{16}*\sqrt{14}=4\sqrt{14}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-4\sqrt{14}}{2*5}=\frac{2-4\sqrt{14}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+4\sqrt{14}}{2*5}=\frac{2+4\sqrt{14}}{10}
$