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

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

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

We move all terms to the left:

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

We multiply parentheses ..

(+6x^2-6x+18x-18)-((7x-3))=0


We calculate terms in parentheses: -((7x-3)), so:

(7x-3)

We get rid of parentheses

7x-3

Back to the equation:

-(7x-3)


We get rid of parentheses

6x^2-6x+18x-7x-18+3=0

We add all the numbers together, and all the variables

6x^2+5x-15=0

a = 6; b = 5; c = -15;
Δ = b2-4ac
Δ = 52-4·6·(-15)
Δ = 385
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{-(5)-\sqrt{385}}{2*6}=\frac{-5-\sqrt{385}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{385}}{2*6}=\frac{-5+\sqrt{385}}{12}
$