7x+31=8x(27x+3)

Solution for 7x+31=8x(27x+3) equation:

7x+31=8x(27x+3)

We move all terms to the left:

7x+31-(8x(27x+3))=0


We calculate terms in parentheses: -(8x(27x+3)), so:

8x(27x+3)

We multiply parentheses

216x^2+24x

Back to the equation:

-(216x^2+24x)


We get rid of parentheses

-216x^2+7x-24x+31=0

We add all the numbers together, and all the variables

-216x^2-17x+31=0

a = -216; b = -17; c = +31;
Δ = b2-4ac
Δ = -172-4·(-216)·31
Δ = 27073
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-17)-\sqrt{27073}}{2*-216}=\frac{17-\sqrt{27073}}{-432}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17)+\sqrt{27073}}{2*-216}=\frac{17+\sqrt{27073}}{-432}
$