3x(2+x)-x+1=35

Solution for 3x(2+x)-x+1=35 equation:

3x(2+x)-x+1=35

We move all terms to the left:

3x(2+x)-x+1-(35)=0

We add all the numbers together, and all the variables

3x(x+2)-x+1-35=0

We add all the numbers together, and all the variables

-1x+3x(x+2)-34=0

We multiply parentheses

3x^2-1x+6x-34=0

We add all the numbers together, and all the variables

3x^2+5x-34=0

a = 3; b = 5; c = -34;
Δ = b2-4ac
Δ = 52-4·3·(-34)
Δ = 433
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{-(5)-\sqrt{433}}{2*3}=\frac{-5-\sqrt{433}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{433}}{2*3}=\frac{-5+\sqrt{433}}{6}
$