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

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

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

We move all terms to the left:

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


We calculate terms in parentheses: -(3x(x-8)+5), so:

3x(x-8)+5

We multiply parentheses

3x^2-24x+5

Back to the equation:

-(3x^2-24x+5)


We get rid of parentheses

-3x^2+x+24x-5=0

We add all the numbers together, and all the variables

-3x^2+25x-5=0

a = -3; b = 25; c = -5;
Δ = b2-4ac
Δ = 252-4·(-3)·(-5)
Δ = 565
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{-(25)-\sqrt{565}}{2*-3}=\frac{-25-\sqrt{565}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(25)+\sqrt{565}}{2*-3}=\frac{-25+\sqrt{565}}{-6}
$