692=4x(x+19)

Solution for 692=4x(x+19) equation:

692=4x(x+19)

We move all terms to the left:

692-(4x(x+19))=0


We calculate terms in parentheses: -(4x(x+19)), so:

4x(x+19)

We multiply parentheses

4x^2+76x

Back to the equation:

-(4x^2+76x)


We get rid of parentheses

-4x^2-76x+692=0

a = -4; b = -76; c = +692;
Δ = b2-4ac
Δ = -762-4·(-4)·692
Δ = 16848
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:

$\sqrt{\Delta}=\sqrt{16848}=\sqrt{1296*13}=\sqrt{1296}*\sqrt{13}=36\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-76)-36\sqrt{13}}{2*-4}=\frac{76-36\sqrt{13}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-76)+36\sqrt{13}}{2*-4}=\frac{76+36\sqrt{13}}{-8}
$