(3x-1)(7x+1)=90

Solution for (3x-1)(7x+1)=90 equation:

(3x-1)(7x+1)=90

We move all terms to the left:

(3x-1)(7x+1)-(90)=0

We multiply parentheses ..

(+21x^2+3x-7x-1)-90=0

We get rid of parentheses

21x^2+3x-7x-1-90=0

We add all the numbers together, and all the variables

21x^2-4x-91=0

a = 21; b = -4; c = -91;
Δ = b2-4ac
Δ = -42-4·21·(-91)
Δ = 7660
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:

$\sqrt{\Delta}=\sqrt{7660}=\sqrt{4*1915}=\sqrt{4}*\sqrt{1915}=2\sqrt{1915}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-2\sqrt{1915}}{2*21}=\frac{4-2\sqrt{1915}}{42}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+2\sqrt{1915}}{2*21}=\frac{4+2\sqrt{1915}}{42}
$