3x+4=7x(x+17)

Solution for 3x+4=7x(x+17) equation:

3x+4=7x(x+17)

We move all terms to the left:

3x+4-(7x(x+17))=0


We calculate terms in parentheses: -(7x(x+17)), so:

7x(x+17)

We multiply parentheses

7x^2+119x

Back to the equation:

-(7x^2+119x)


We get rid of parentheses

-7x^2+3x-119x+4=0

We add all the numbers together, and all the variables

-7x^2-116x+4=0

a = -7; b = -116; c = +4;
Δ = b2-4ac
Δ = -1162-4·(-7)·4
Δ = 13568
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:

$\sqrt{\Delta}=\sqrt{13568}=\sqrt{256*53}=\sqrt{256}*\sqrt{53}=16\sqrt{53}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-116)-16\sqrt{53}}{2*-7}=\frac{116-16\sqrt{53}}{-14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-116)+16\sqrt{53}}{2*-7}=\frac{116+16\sqrt{53}}{-14}
$