3x+8=5(x-4)x

Solution for 3x+8=5(x-4)x equation:

3x+8=5(x-4)x

We move all terms to the left:

3x+8-(5(x-4)x)=0


We calculate terms in parentheses: -(5(x-4)x), so:

5(x-4)x

We multiply parentheses

5x^2-20x

Back to the equation:

-(5x^2-20x)


We get rid of parentheses

-5x^2+3x+20x+8=0

We add all the numbers together, and all the variables

-5x^2+23x+8=0

a = -5; b = 23; c = +8;
Δ = b2-4ac
Δ = 232-4·(-5)·8
Δ = 689
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{-(23)-\sqrt{689}}{2*-5}=\frac{-23-\sqrt{689}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(23)+\sqrt{689}}{2*-5}=\frac{-23+\sqrt{689}}{-10}
$