3x(x+8)+x=90

Solution for 3x(x+8)+x=90 equation:

3x(x+8)+x=90

We move all terms to the left:

3x(x+8)+x-(90)=0

We add all the numbers together, and all the variables

x+3x(x+8)-90=0

We multiply parentheses

3x^2+x+24x-90=0

We add all the numbers together, and all the variables

3x^2+25x-90=0

a = 3; b = 25; c = -90;
Δ = b2-4ac
Δ = 252-4·3·(-90)
Δ = 1705
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{1705}}{2*3}=\frac{-25-\sqrt{1705}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(25)+\sqrt{1705}}{2*3}=\frac{-25+\sqrt{1705}}{6}
$