(x+4)(2x-1)=35

Solution for (x+4)(2x-1)=35 equation:

(x+4)(2x-1)=35

We move all terms to the left:

(x+4)(2x-1)-(35)=0

We multiply parentheses ..

(+2x^2-1x+8x-4)-35=0

We get rid of parentheses

2x^2-1x+8x-4-35=0

We add all the numbers together, and all the variables

2x^2+7x-39=0

a = 2; b = 7; c = -39;
Δ = b2-4ac
Δ = 72-4·2·(-39)
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-19}{2*2}=\frac{-26}{4}
=-6+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+19}{2*2}=\frac{12}{4}
=3
$