5x(x+1)+7(x+3)=146

Solution for 5x(x+1)+7(x+3)=146 equation:

5x(x+1)+7(x+3)=146

We move all terms to the left:

5x(x+1)+7(x+3)-(146)=0

We multiply parentheses

5x^2+5x+7x+21-146=0

We add all the numbers together, and all the variables

5x^2+12x-125=0

a = 5; b = 12; c = -125;
Δ = b2-4ac
Δ = 122-4·5·(-125)
Δ = 2644
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:

$\sqrt{\Delta}=\sqrt{2644}=\sqrt{4*661}=\sqrt{4}*\sqrt{661}=2\sqrt{661}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-2\sqrt{661}}{2*5}=\frac{-12-2\sqrt{661}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+2\sqrt{661}}{2*5}=\frac{-12+2\sqrt{661}}{10}
$