(7x-5)(x+3)=90

Solution for (7x-5)(x+3)=90 equation:

(7x-5)(x+3)=90

We move all terms to the left:

(7x-5)(x+3)-(90)=0

We multiply parentheses ..

(+7x^2+21x-5x-15)-90=0

We get rid of parentheses

7x^2+21x-5x-15-90=0

We add all the numbers together, and all the variables

7x^2+16x-105=0

a = 7; b = 16; c = -105;
Δ = b2-4ac
Δ = 162-4·7·(-105)
Δ = 3196
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:

$\sqrt{\Delta}=\sqrt{3196}=\sqrt{4*799}=\sqrt{4}*\sqrt{799}=2\sqrt{799}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-2\sqrt{799}}{2*7}=\frac{-16-2\sqrt{799}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+2\sqrt{799}}{2*7}=\frac{-16+2\sqrt{799}}{14}
$