4x+7=6(x-2)3x

Solution for 4x+7=6(x-2)3x equation:

4x+7=6(x-2)3x

We move all terms to the left:

4x+7-(6(x-2)3x)=0


We calculate terms in parentheses: -(6(x-2)3x), so:

6(x-2)3x

We multiply parentheses

18x^2-36x

Back to the equation:

-(18x^2-36x)


We get rid of parentheses

-18x^2+4x+36x+7=0

We add all the numbers together, and all the variables

-18x^2+40x+7=0

a = -18; b = 40; c = +7;
Δ = b2-4ac
Δ = 402-4·(-18)·7
Δ = 2104
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:

$\sqrt{\Delta}=\sqrt{2104}=\sqrt{4*526}=\sqrt{4}*\sqrt{526}=2\sqrt{526}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-2\sqrt{526}}{2*-18}=\frac{-40-2\sqrt{526}}{-36}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+2\sqrt{526}}{2*-18}=\frac{-40+2\sqrt{526}}{-36}
$