-105x+3x^2=534

Solution for -105x+3x^2=534 equation:

-105x+3x^2=534

We move all terms to the left:

-105x+3x^2-(534)=0

a = 3; b = -105; c = -534;
Δ = b2-4ac
Δ = -1052-4·3·(-534)
Δ = 17433
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:

$\sqrt{\Delta}=\sqrt{17433}=\sqrt{9*1937}=\sqrt{9}*\sqrt{1937}=3\sqrt{1937}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-105)-3\sqrt{1937}}{2*3}=\frac{105-3\sqrt{1937}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-105)+3\sqrt{1937}}{2*3}=\frac{105+3\sqrt{1937}}{6}
$