(15x-2)(7x+4)=90

Solution for (15x-2)(7x+4)=90 equation:

(15x-2)(7x+4)=90

We move all terms to the left:

(15x-2)(7x+4)-(90)=0

We multiply parentheses ..

(+105x^2+60x-14x-8)-90=0

We get rid of parentheses

105x^2+60x-14x-8-90=0

We add all the numbers together, and all the variables

105x^2+46x-98=0

a = 105; b = 46; c = -98;
Δ = b2-4ac
Δ = 462-4·105·(-98)
Δ = 43276
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:

$\sqrt{\Delta}=\sqrt{43276}=\sqrt{4*10819}=\sqrt{4}*\sqrt{10819}=2\sqrt{10819}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(46)-2\sqrt{10819}}{2*105}=\frac{-46-2\sqrt{10819}}{210}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(46)+2\sqrt{10819}}{2*105}=\frac{-46+2\sqrt{10819}}{210}
$