(4n-3)(2n+5)=22

Solution for (4n-3)(2n+5)=22 equation:

(4n-3)(2n+5)=22

We move all terms to the left:

(4n-3)(2n+5)-(22)=0

We multiply parentheses ..

(+8n^2+20n-6n-15)-22=0

We get rid of parentheses

8n^2+20n-6n-15-22=0

We add all the numbers together, and all the variables

8n^2+14n-37=0

a = 8; b = 14; c = -37;
Δ = b2-4ac
Δ = 142-4·8·(-37)
Δ = 1380
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1380}=\sqrt{4*345}=\sqrt{4}*\sqrt{345}=2\sqrt{345}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-2\sqrt{345}}{2*8}=\frac{-14-2\sqrt{345}}{16}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+2\sqrt{345}}{2*8}=\frac{-14+2\sqrt{345}}{16}
$