6x+10=2x(3x+4)

Solution for 6x+10=2x(3x+4) equation:

6x+10=2x(3x+4)

We move all terms to the left:

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


We calculate terms in parentheses: -(2x(3x+4)), so:

2x(3x+4)

We multiply parentheses

6x^2+8x

Back to the equation:

-(6x^2+8x)


We get rid of parentheses

-6x^2+6x-8x+10=0

We add all the numbers together, and all the variables

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

a = -6; b = -2; c = +10;
Δ = b2-4ac
Δ = -22-4·(-6)·10
Δ = 244
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:

$\sqrt{\Delta}=\sqrt{244}=\sqrt{4*61}=\sqrt{4}*\sqrt{61}=2\sqrt{61}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{61}}{2*-6}=\frac{2-2\sqrt{61}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{61}}{2*-6}=\frac{2+2\sqrt{61}}{-12}
$