-3x(x-2)+4=2x-10

Solution for -3x(x-2)+4=2x-10 equation:

-3x(x-2)+4=2x-10

We move all terms to the left:

-3x(x-2)+4-(2x-10)=0

We multiply parentheses

-3x^2+6x-(2x-10)+4=0

We get rid of parentheses

-3x^2+6x-2x+10+4=0

We add all the numbers together, and all the variables

-3x^2+4x+14=0

a = -3; b = 4; c = +14;
Δ = b2-4ac
Δ = 42-4·(-3)·14
Δ = 184
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:

$\sqrt{\Delta}=\sqrt{184}=\sqrt{4*46}=\sqrt{4}*\sqrt{46}=2\sqrt{46}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-2\sqrt{46}}{2*-3}=\frac{-4-2\sqrt{46}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+2\sqrt{46}}{2*-3}=\frac{-4+2\sqrt{46}}{-6}
$