2(1.5x+10)=3(x+6)x=

Solution for 2(1.5x+10)=3(x+6)x= equation:

2(1.5x+10)=3(x+6)x=

We move all terms to the left:

2(1.5x+10)-(3(x+6)x)=0

We multiply parentheses

2x-(3(x+6)x)+20=0


We calculate terms in parentheses: -(3(x+6)x), so:

3(x+6)x

We multiply parentheses

3x^2+18x

Back to the equation:

-(3x^2+18x)


We get rid of parentheses

-3x^2+2x-18x+20=0

We add all the numbers together, and all the variables

-3x^2-16x+20=0

a = -3; b = -16; c = +20;
Δ = b2-4ac
Δ = -162-4·(-3)·20
Δ = 496
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:

$\sqrt{\Delta}=\sqrt{496}=\sqrt{16*31}=\sqrt{16}*\sqrt{31}=4\sqrt{31}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-4\sqrt{31}}{2*-3}=\frac{16-4\sqrt{31}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+4\sqrt{31}}{2*-3}=\frac{16+4\sqrt{31}}{-6}
$