90+(2x+14)(x+7)=180

Solution for 90+(2x+14)(x+7)=180 equation:

90+(2x+14)(x+7)=180

We move all terms to the left:

90+(2x+14)(x+7)-(180)=0

We add all the numbers together, and all the variables

(2x+14)(x+7)-90=0

We multiply parentheses ..

(+2x^2+14x+14x+98)-90=0

We get rid of parentheses

2x^2+14x+14x+98-90=0

We add all the numbers together, and all the variables

2x^2+28x+8=0

a = 2; b = 28; c = +8;
Δ = b2-4ac
Δ = 282-4·2·8
Δ = 720
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:

$\sqrt{\Delta}=\sqrt{720}=\sqrt{144*5}=\sqrt{144}*\sqrt{5}=12\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(28)-12\sqrt{5}}{2*2}=\frac{-28-12\sqrt{5}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(28)+12\sqrt{5}}{2*2}=\frac{-28+12\sqrt{5}}{4}
$