x2-345x-234=0

Solution for x2-345x-234=0 equation:

x2-345x-234=0

We add all the numbers together, and all the variables

x^2-345x-234=0

a = 1; b = -345; c = -234;
Δ = b2-4ac
Δ = -3452-4·1·(-234)
Δ = 119961
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{119961}=\sqrt{81*1481}=\sqrt{81}*\sqrt{1481}=9\sqrt{1481}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-345)-9\sqrt{1481}}{2*1}=\frac{345-9\sqrt{1481}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-345)+9\sqrt{1481}}{2*1}=\frac{345+9\sqrt{1481}}{2}
$