3x^2=-6x+71

Solution for 3x^2=-6x+71 equation:

3x^2=-6x+71

We move all terms to the left:

3x^2-(-6x+71)=0

We get rid of parentheses

3x^2+6x-71=0

a = 3; b = 6; c = -71;
Δ = b2-4ac
Δ = 62-4·3·(-71)
Δ = 888
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:

$\sqrt{\Delta}=\sqrt{888}=\sqrt{4*222}=\sqrt{4}*\sqrt{222}=2\sqrt{222}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{222}}{2*3}=\frac{-6-2\sqrt{222}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{222}}{2*3}=\frac{-6+2\sqrt{222}}{6}
$