6x(x+3)=4x+21

Solution for 6x(x+3)=4x+21 equation:

6x(x+3)=4x+21

We move all terms to the left:

6x(x+3)-(4x+21)=0

We multiply parentheses

6x^2+18x-(4x+21)=0

We get rid of parentheses

6x^2+18x-4x-21=0

We add all the numbers together, and all the variables

6x^2+14x-21=0

a = 6; b = 14; c = -21;
Δ = b2-4ac
Δ = 142-4·6·(-21)
Δ = 700
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:

$\sqrt{\Delta}=\sqrt{700}=\sqrt{100*7}=\sqrt{100}*\sqrt{7}=10\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-10\sqrt{7}}{2*6}=\frac{-14-10\sqrt{7}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+10\sqrt{7}}{2*6}=\frac{-14+10\sqrt{7}}{12}
$