(19x-18)(7x+1)=(10x-9)

Solution for (19x-18)(7x+1)=(10x-9) equation:

(19x-18)(7x+1)=(10x-9)

We move all terms to the left:

(19x-18)(7x+1)-((10x-9))=0

We multiply parentheses ..

(+133x^2+19x-126x-18)-((10x-9))=0


We calculate terms in parentheses: -((10x-9)), so:

(10x-9)

We get rid of parentheses

10x-9

Back to the equation:

-(10x-9)


We get rid of parentheses

133x^2+19x-126x-10x-18+9=0

We add all the numbers together, and all the variables

133x^2-117x-9=0

a = 133; b = -117; c = -9;
Δ = b2-4ac
Δ = -1172-4·133·(-9)
Δ = 18477
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{18477}=\sqrt{9*2053}=\sqrt{9}*\sqrt{2053}=3\sqrt{2053}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-117)-3\sqrt{2053}}{2*133}=\frac{117-3\sqrt{2053}}{266}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-117)+3\sqrt{2053}}{2*133}=\frac{117+3\sqrt{2053}}{266}
$