2+x(3x+8-1)=45

Solution for 2+x(3x+8-1)=45 equation:

2+x(3x+8-1)=45

We move all terms to the left:

2+x(3x+8-1)-(45)=0

We add all the numbers together, and all the variables

x(3x+7)+2-45=0

We add all the numbers together, and all the variables

x(3x+7)-43=0

We multiply parentheses

3x^2+7x-43=0

a = 3; b = 7; c = -43;
Δ = b2-4ac
Δ = 72-4·3·(-43)
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{-(7)-\sqrt{565}}{2*3}=\frac{-7-\sqrt{565}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{565}}{2*3}=\frac{-7+\sqrt{565}}{6}
$