(3x+5)(7-x)=8

Solution for (3x+5)(7-x)=8 equation:

(3x+5)(7-x)=8

We move all terms to the left:

(3x+5)(7-x)-(8)=0

We add all the numbers together, and all the variables

(3x+5)(-1x+7)-8=0

We multiply parentheses ..

(-3x^2+21x-5x+35)-8=0

We get rid of parentheses

-3x^2+21x-5x+35-8=0

We add all the numbers together, and all the variables

-3x^2+16x+27=0

a = -3; b = 16; c = +27;
Δ = b2-4ac
Δ = 162-4·(-3)·27
Δ = 580
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:

$\sqrt{\Delta}=\sqrt{580}=\sqrt{4*145}=\sqrt{4}*\sqrt{145}=2\sqrt{145}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-2\sqrt{145}}{2*-3}=\frac{-16-2\sqrt{145}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+2\sqrt{145}}{2*-3}=\frac{-16+2\sqrt{145}}{-6}
$