(2x+1)(x+14)=90

Solution for (2x+1)(x+14)=90 equation:

(2x+1)(x+14)=90

We move all terms to the left:

(2x+1)(x+14)-(90)=0

We multiply parentheses ..

(+2x^2+28x+x+14)-90=0

We get rid of parentheses

2x^2+28x+x+14-90=0

We add all the numbers together, and all the variables

2x^2+29x-76=0

a = 2; b = 29; c = -76;
Δ = b2-4ac
Δ = 292-4·2·(-76)
Δ = 1449
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:

$\sqrt{\Delta}=\sqrt{1449}=\sqrt{9*161}=\sqrt{9}*\sqrt{161}=3\sqrt{161}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(29)-3\sqrt{161}}{2*2}=\frac{-29-3\sqrt{161}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(29)+3\sqrt{161}}{2*2}=\frac{-29+3\sqrt{161}}{4}
$