3x(4x-7=27)

Solution for 3x(4x-7=27) equation:

3x(4x-7=27)

We move all terms to the left:

3x(4x-7-(27))=0

We add all the numbers together, and all the variables

3x(4x-34)=0

We multiply parentheses

12x^2-102x=0

a = 12; b = -102; c = 0;
Δ = b2-4ac
Δ = -1022-4·12·0
Δ = 10404
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{10404}=102$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-102)-102}{2*12}=\frac{0}{24}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-102)+102}{2*12}=\frac{204}{24}
=8+1/2
$