(3x-7)(x+8)=90

Solution for (3x-7)(x+8)=90 equation:

(3x-7)(x+8)=90

We move all terms to the left:

(3x-7)(x+8)-(90)=0

We multiply parentheses ..

(+3x^2+24x-7x-56)-90=0

We get rid of parentheses

3x^2+24x-7x-56-90=0

We add all the numbers together, and all the variables

3x^2+17x-146=0

a = 3; b = 17; c = -146;
Δ = b2-4ac
Δ = 172-4·3·(-146)
Δ = 2041
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(17)-\sqrt{2041}}{2*3}=\frac{-17-\sqrt{2041}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+\sqrt{2041}}{2*3}=\frac{-17+\sqrt{2041}}{6}
$