(7+35x)(6+24x)=13

Solution for (7+35x)(6+24x)=13 equation:

(7+35x)(6+24x)=13

We move all terms to the left:

(7+35x)(6+24x)-(13)=0

We add all the numbers together, and all the variables

(35x+7)(24x+6)-13=0

We multiply parentheses ..

(+840x^2+210x+168x+42)-13=0

We get rid of parentheses

840x^2+210x+168x+42-13=0

We add all the numbers together, and all the variables

840x^2+378x+29=0

a = 840; b = 378; c = +29;
Δ = b2-4ac
Δ = 3782-4·840·29
Δ = 45444
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:

$\sqrt{\Delta}=\sqrt{45444}=\sqrt{4*11361}=\sqrt{4}*\sqrt{11361}=2\sqrt{11361}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(378)-2\sqrt{11361}}{2*840}=\frac{-378-2\sqrt{11361}}{1680}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(378)+2\sqrt{11361}}{2*840}=\frac{-378+2\sqrt{11361}}{1680}
$