(x-7)(x+183)=(3x-10)

Solution for (x-7)(x+183)=(3x-10) equation:

(x-7)(x+183)=(3x-10)

We move all terms to the left:

(x-7)(x+183)-((3x-10))=0

We multiply parentheses ..

(+x^2+183x-7x-1281)-((3x-10))=0


We calculate terms in parentheses: -((3x-10)), so:

(3x-10)

We get rid of parentheses

3x-10

Back to the equation:

-(3x-10)


We get rid of parentheses

x^2+183x-7x-3x-1281+10=0

We add all the numbers together, and all the variables

x^2+173x-1271=0

a = 1; b = 173; c = -1271;
Δ = b2-4ac
Δ = 1732-4·1·(-1271)
Δ = 35013
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{-(173)-\sqrt{35013}}{2*1}=\frac{-173-\sqrt{35013}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(173)+\sqrt{35013}}{2*1}=\frac{-173+\sqrt{35013}}{2}
$