(7x-9)(4x+22)=90

Solution for (7x-9)(4x+22)=90 equation:

(7x-9)(4x+22)=90

We move all terms to the left:

(7x-9)(4x+22)-(90)=0

We multiply parentheses ..

(+28x^2+154x-36x-198)-90=0

We get rid of parentheses

28x^2+154x-36x-198-90=0

We add all the numbers together, and all the variables

28x^2+118x-288=0

a = 28; b = 118; c = -288;
Δ = b2-4ac
Δ = 1182-4·28·(-288)
Δ = 46180
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:

$\sqrt{\Delta}=\sqrt{46180}=\sqrt{4*11545}=\sqrt{4}*\sqrt{11545}=2\sqrt{11545}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(118)-2\sqrt{11545}}{2*28}=\frac{-118-2\sqrt{11545}}{56}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(118)+2\sqrt{11545}}{2*28}=\frac{-118+2\sqrt{11545}}{56}
$