(10x+9)(3x+13)=x+4

Solution for (10x+9)(3x+13)=x+4 equation:

(10x+9)(3x+13)=x+4

We move all terms to the left:

(10x+9)(3x+13)-(x+4)=0

We get rid of parentheses

(10x+9)(3x+13)-x-4=0

We multiply parentheses ..

(+30x^2+130x+27x+117)-x-4=0

We add all the numbers together, and all the variables

(+30x^2+130x+27x+117)-1x-4=0

We get rid of parentheses

30x^2+130x+27x-1x+117-4=0

We add all the numbers together, and all the variables

30x^2+156x+113=0

a = 30; b = 156; c = +113;
Δ = b2-4ac
Δ = 1562-4·30·113
Δ = 10776
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:

$\sqrt{\Delta}=\sqrt{10776}=\sqrt{4*2694}=\sqrt{4}*\sqrt{2694}=2\sqrt{2694}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(156)-2\sqrt{2694}}{2*30}=\frac{-156-2\sqrt{2694}}{60}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(156)+2\sqrt{2694}}{2*30}=\frac{-156+2\sqrt{2694}}{60}
$