1x+(x+7)+(1x+7x2)=53

Solution for 1x+(x+7)+(1x+7x2)=53 equation:

1x+(x+7)+(1x+7x^2)=53

We move all terms to the left:

1x+(x+7)+(1x+7x^2)-(53)=0

We add all the numbers together, and all the variables

(1x+7x^2)+x+(x+7)-53=0

We get rid of parentheses

7x^2+1x+x+x+7-53=0

We add all the numbers together, and all the variables

7x^2+3x-46=0

a = 7; b = 3; c = -46;
Δ = b2-4ac
Δ = 32-4·7·(-46)
Δ = 1297
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{-(3)-\sqrt{1297}}{2*7}=\frac{-3-\sqrt{1297}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{1297}}{2*7}=\frac{-3+\sqrt{1297}}{14}
$