3x(x-8)+10x=67

Solution for 3x(x-8)+10x=67 equation:

3x(x-8)+10x=67

We move all terms to the left:

3x(x-8)+10x-(67)=0

We add all the numbers together, and all the variables

10x+3x(x-8)-67=0

We multiply parentheses

3x^2+10x-24x-67=0

We add all the numbers together, and all the variables

3x^2-14x-67=0

a = 3; b = -14; c = -67;
Δ = b2-4ac
Δ = -142-4·3·(-67)
Δ = 1000
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:

$\sqrt{\Delta}=\sqrt{1000}=\sqrt{100*10}=\sqrt{100}*\sqrt{10}=10\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-10\sqrt{10}}{2*3}=\frac{14-10\sqrt{10}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+10\sqrt{10}}{2*3}=\frac{14+10\sqrt{10}}{6}
$