10-3x-1=7+3x2

Solution for 10-3x-1=7+3x2 equation:

10-3x-1=7+3x^2

We move all terms to the left:

10-3x-1-(7+3x^2)=0

We add all the numbers together, and all the variables

-(7+3x^2)-3x+9=0

We get rid of parentheses

-3x^2-3x-7+9=0

We add all the numbers together, and all the variables

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

a = -3; b = -3; c = +2;
Δ = b2-4ac
Δ = -32-4·(-3)·2
Δ = 33
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{-(-3)-\sqrt{33}}{2*-3}=\frac{3-\sqrt{33}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{33}}{2*-3}=\frac{3+\sqrt{33}}{-6}
$