(2x+9)(x+7)=150

Solution for (2x+9)(x+7)=150 equation:

(2x+9)(x+7)=150

We move all terms to the left:

(2x+9)(x+7)-(150)=0

We multiply parentheses ..

(+2x^2+14x+9x+63)-150=0

We get rid of parentheses

2x^2+14x+9x+63-150=0

We add all the numbers together, and all the variables

2x^2+23x-87=0

a = 2; b = 23; c = -87;
Δ = b2-4ac
Δ = 232-4·2·(-87)
Δ = 1225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1225}=35$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(23)-35}{2*2}=\frac{-58}{4}
=-14+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(23)+35}{2*2}=\frac{12}{4}
=3
$