10-3x(x=6)

Solution for 10-3x(x=6) equation:

10-3x(x=6)

We move all terms to the left:

10-3x(x-(6))=0

We multiply parentheses

-3x^2+18x+10=0

a = -3; b = 18; c = +10;
Δ = b2-4ac
Δ = 182-4·(-3)·10
Δ = 444
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:

$\sqrt{\Delta}=\sqrt{444}=\sqrt{4*111}=\sqrt{4}*\sqrt{111}=2\sqrt{111}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-2\sqrt{111}}{2*-3}=\frac{-18-2\sqrt{111}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+2\sqrt{111}}{2*-3}=\frac{-18+2\sqrt{111}}{-6}
$