34+x2-45-12=43x+2

Solution for 34+x2-45-12=43x+2 equation:

34+x2-45-12=43x+2

We move all terms to the left:

34+x2-45-12-(43x+2)=0

We add all the numbers together, and all the variables

x^2-(43x+2)-23=0

We get rid of parentheses

x^2-43x-2-23=0

We add all the numbers together, and all the variables

x^2-43x-25=0

a = 1; b = -43; c = -25;
Δ = b2-4ac
Δ = -432-4·1·(-25)
Δ = 1949
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{-(-43)-\sqrt{1949}}{2*1}=\frac{43-\sqrt{1949}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-43)+\sqrt{1949}}{2*1}=\frac{43+\sqrt{1949}}{2}
$