(8x+7)(2x+8)=45

Solution for (8x+7)(2x+8)=45 equation:

(8x+7)(2x+8)=45

We move all terms to the left:

(8x+7)(2x+8)-(45)=0

We multiply parentheses ..

(+16x^2+64x+14x+56)-45=0

We get rid of parentheses

16x^2+64x+14x+56-45=0

We add all the numbers together, and all the variables

16x^2+78x+11=0

a = 16; b = 78; c = +11;
Δ = b2-4ac
Δ = 782-4·16·11
Δ = 5380
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:

$\sqrt{\Delta}=\sqrt{5380}=\sqrt{4*1345}=\sqrt{4}*\sqrt{1345}=2\sqrt{1345}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(78)-2\sqrt{1345}}{2*16}=\frac{-78-2\sqrt{1345}}{32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(78)+2\sqrt{1345}}{2*16}=\frac{-78+2\sqrt{1345}}{32}
$