(X-2)(3x+1)=150

Solution for (X-2)(3x+1)=150 equation:

(X-2)(3X+1)=150

We move all terms to the left:

(X-2)(3X+1)-(150)=0

We multiply parentheses ..

(+3X^2+X-6X-2)-150=0

We get rid of parentheses

3X^2+X-6X-2-150=0

We add all the numbers together, and all the variables

3X^2-5X-152=0

a = 3; b = -5; c = -152;
Δ = b2-4ac
Δ = -52-4·3·(-152)
Δ = 1849
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1849}=43$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-43}{2*3}=\frac{-38}{6}
=-6+1/3
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+43}{2*3}=\frac{48}{6}
=8
$