3x^2-10x=456

Solution for 3x^2-10x=456 equation:

3x^2-10x=456

We move all terms to the left:

3x^2-10x-(456)=0

a = 3; b = -10; c = -456;
Δ = b2-4ac
Δ = -102-4·3·(-456)
Δ = 5572
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:

$\sqrt{\Delta}=\sqrt{5572}=\sqrt{4*1393}=\sqrt{4}*\sqrt{1393}=2\sqrt{1393}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{1393}}{2*3}=\frac{10-2\sqrt{1393}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{1393}}{2*3}=\frac{10+2\sqrt{1393}}{6}
$