(x+3)(x+4)=342

Solution for (x+3)(x+4)=342 equation:

(x+3)(x+4)=342

We move all terms to the left:

(x+3)(x+4)-(342)=0

We multiply parentheses ..

(+x^2+4x+3x+12)-342=0

We get rid of parentheses

x^2+4x+3x+12-342=0

We add all the numbers together, and all the variables

x^2+7x-330=0

a = 1; b = 7; c = -330;
Δ = b2-4ac
Δ = 72-4·1·(-330)
Δ = 1369
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1369}=37$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-37}{2*1}=\frac{-44}{2}
=-22
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+37}{2*1}=\frac{30}{2}
=15
$