(6x+22)(7x+16)=90

Solution for (6x+22)(7x+16)=90 equation:

(6x+22)(7x+16)=90

We move all terms to the left:

(6x+22)(7x+16)-(90)=0

We multiply parentheses ..

(+42x^2+96x+154x+352)-90=0

We get rid of parentheses

42x^2+96x+154x+352-90=0

We add all the numbers together, and all the variables

42x^2+250x+262=0

a = 42; b = 250; c = +262;
Δ = b2-4ac
Δ = 2502-4·42·262
Δ = 18484
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:

$\sqrt{\Delta}=\sqrt{18484}=\sqrt{4*4621}=\sqrt{4}*\sqrt{4621}=2\sqrt{4621}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(250)-2\sqrt{4621}}{2*42}=\frac{-250-2\sqrt{4621}}{84}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(250)+2\sqrt{4621}}{2*42}=\frac{-250+2\sqrt{4621}}{84}
$