(7x-19)(4x+2)=90

Solution for (7x-19)(4x+2)=90 equation:

(7x-19)(4x+2)=90

We move all terms to the left:

(7x-19)(4x+2)-(90)=0

We multiply parentheses ..

(+28x^2+14x-76x-38)-90=0

We get rid of parentheses

28x^2+14x-76x-38-90=0

We add all the numbers together, and all the variables

28x^2-62x-128=0

a = 28; b = -62; c = -128;
Δ = b2-4ac
Δ = -622-4·28·(-128)
Δ = 18180
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:

$\sqrt{\Delta}=\sqrt{18180}=\sqrt{36*505}=\sqrt{36}*\sqrt{505}=6\sqrt{505}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-62)-6\sqrt{505}}{2*28}=\frac{62-6\sqrt{505}}{56}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-62)+6\sqrt{505}}{2*28}=\frac{62+6\sqrt{505}}{56}
$