6(x+5)=3x(x-14)

Solution for 6(x+5)=3x(x-14) equation:

6(x+5)=3x(x-14)

We move all terms to the left:

6(x+5)-(3x(x-14))=0

We multiply parentheses

6x-(3x(x-14))+30=0


We calculate terms in parentheses: -(3x(x-14)), so:

3x(x-14)

We multiply parentheses

3x^2-42x

Back to the equation:

-(3x^2-42x)


We get rid of parentheses

-3x^2+6x+42x+30=0

We add all the numbers together, and all the variables

-3x^2+48x+30=0

a = -3; b = 48; c = +30;
Δ = b2-4ac
Δ = 482-4·(-3)·30
Δ = 2664
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:

$\sqrt{\Delta}=\sqrt{2664}=\sqrt{36*74}=\sqrt{36}*\sqrt{74}=6\sqrt{74}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(48)-6\sqrt{74}}{2*-3}=\frac{-48-6\sqrt{74}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(48)+6\sqrt{74}}{2*-3}=\frac{-48+6\sqrt{74}}{-6}
$