(x+5)(2x-1)=76

Solution for (x+5)(2x-1)=76 equation:

(x+5)(2x-1)=76

We move all terms to the left:

(x+5)(2x-1)-(76)=0

We multiply parentheses ..

(+2x^2-1x+10x-5)-76=0

We get rid of parentheses

2x^2-1x+10x-5-76=0

We add all the numbers together, and all the variables

2x^2+9x-81=0

a = 2; b = 9; c = -81;
Δ = b2-4ac
Δ = 92-4·2·(-81)
Δ = 729
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{729}=27$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-27}{2*2}=\frac{-36}{4}
=-9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+27}{2*2}=\frac{18}{4}
=4+1/2
$