(19x+3)(9x+16)=(6x+15)

Solution for (19x+3)(9x+16)=(6x+15) equation:

(19x+3)(9x+16)=(6x+15)

We move all terms to the left:

(19x+3)(9x+16)-((6x+15))=0

We multiply parentheses ..

(+171x^2+304x+27x+48)-((6x+15))=0


We calculate terms in parentheses: -((6x+15)), so:

(6x+15)

We get rid of parentheses

6x+15

Back to the equation:

-(6x+15)


We get rid of parentheses

171x^2+304x+27x-6x+48-15=0

We add all the numbers together, and all the variables

171x^2+325x+33=0

a = 171; b = 325; c = +33;
Δ = b2-4ac
Δ = 3252-4·171·33
Δ = 83053
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:

$\sqrt{\Delta}=\sqrt{83053}=\sqrt{529*157}=\sqrt{529}*\sqrt{157}=23\sqrt{157}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(325)-23\sqrt{157}}{2*171}=\frac{-325-23\sqrt{157}}{342}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(325)+23\sqrt{157}}{2*171}=\frac{-325+23\sqrt{157}}{342}
$