(x-1)(7x+3)=-18(x-1)

Solution for (x-1)(7x+3)=-18(x-1) equation:

(x-1)(7x+3)=-18(x-1)

We move all terms to the left:

(x-1)(7x+3)-(-18(x-1))=0

We multiply parentheses ..

(+7x^2+3x-7x-3)-(-18(x-1))=0


We calculate terms in parentheses: -(-18(x-1)), so:

-18(x-1)

We multiply parentheses

-18x+18

Back to the equation:

-(-18x+18)


We get rid of parentheses

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

We add all the numbers together, and all the variables

7x^2+14x-21=0

a = 7; b = 14; c = -21;
Δ = b2-4ac
Δ = 142-4·7·(-21)
Δ = 784
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{784}=28$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-28}{2*7}=\frac{-42}{14}
=-3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+28}{2*7}=\frac{14}{14}
=1
$