3x^2=6-10x

Solution for 3x^2=6-10x equation:

3x^2=6-10x

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We get rid of parentheses

3x^2+10x-6=0

a = 3; b = 10; c = -6;
Δ = b2-4ac
Δ = 102-4·3·(-6)
Δ = 172
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:

$\sqrt{\Delta}=\sqrt{172}=\sqrt{4*43}=\sqrt{4}*\sqrt{43}=2\sqrt{43}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{43}}{2*3}=\frac{-10-2\sqrt{43}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{43}}{2*3}=\frac{-10+2\sqrt{43}}{6}
$