5x(x-4)=-3x+44

Solution for 5x(x-4)=-3x+44 equation:

5x(x-4)=-3x+44

We move all terms to the left:

5x(x-4)-(-3x+44)=0

We multiply parentheses

5x^2-20x-(-3x+44)=0

We get rid of parentheses

5x^2-20x+3x-44=0

We add all the numbers together, and all the variables

5x^2-17x-44=0

a = 5; b = -17; c = -44;
Δ = b2-4ac
Δ = -172-4·5·(-44)
Δ = 1169
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{1169}}{2*5}=\frac{17-\sqrt{1169}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17)+\sqrt{1169}}{2*5}=\frac{17+\sqrt{1169}}{10}
$