x^2+x+7x+7=144

Solution for x^2+x+7x+7=144 equation:

x^2+x+7x+7=144

We move all terms to the left:

x^2+x+7x+7-(144)=0

We add all the numbers together, and all the variables

x^2+8x-137=0

a = 1; b = 8; c = -137;
Δ = b2-4ac
Δ = 82-4·1·(-137)
Δ = 612
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:

$\sqrt{\Delta}=\sqrt{612}=\sqrt{36*17}=\sqrt{36}*\sqrt{17}=6\sqrt{17}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-6\sqrt{17}}{2*1}=\frac{-8-6\sqrt{17}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+6\sqrt{17}}{2*1}=\frac{-8+6\sqrt{17}}{2}
$