7(0.3x-0.9)=6x(18+4x)

Solution for 7(0.3x-0.9)=6x(18+4x) equation:

7(0.3x-0.9)=6x(18+4x)

We move all terms to the left:

7(0.3x-0.9)-(6x(18+4x))=0

We add all the numbers together, and all the variables

7(0.3x-0.9)-(6x(4x+18))=0

We multiply parentheses

0x-(6x(4x+18))-6.3=0


We calculate terms in parentheses: -(6x(4x+18)), so:

6x(4x+18)

We multiply parentheses

24x^2+108x

Back to the equation:

-(24x^2+108x)


We add all the numbers together, and all the variables

x-(24x^2+108x)-6.3=0

We get rid of parentheses

-24x^2+x-108x-6.3=0

We add all the numbers together, and all the variables

-24x^2-107x-6.3=0

a = -24; b = -107; c = -6.3;
Δ = b2-4ac
Δ = -1072-4·(-24)·(-6.3)
Δ = 10844.2
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-107)-\sqrt{10844.2}}{2*-24}=\frac{107-\sqrt{10844.2}}{-48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-107)+\sqrt{10844.2}}{2*-24}=\frac{107+\sqrt{10844.2}}{-48}
$