3x^2-60x=-257

Solution for 3x^2-60x=-257 equation:

3x^2-60x=-257

We move all terms to the left:

3x^2-60x-(-257)=0

We add all the numbers together, and all the variables

3x^2-60x+257=0

a = 3; b = -60; c = +257;
Δ = b2-4ac
Δ = -602-4·3·257
Δ = 516
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:

$\sqrt{\Delta}=\sqrt{516}=\sqrt{4*129}=\sqrt{4}*\sqrt{129}=2\sqrt{129}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-60)-2\sqrt{129}}{2*3}=\frac{60-2\sqrt{129}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+2\sqrt{129}}{2*3}=\frac{60+2\sqrt{129}}{6}
$