7x^2+x=100x-92

Solution for 7x^2+x=100x-92 equation:

7x^2+x=100x-92

We move all terms to the left:

7x^2+x-(100x-92)=0

We get rid of parentheses

7x^2+x-100x+92=0

We add all the numbers together, and all the variables

7x^2-99x+92=0

a = 7; b = -99; c = +92;
Δ = b2-4ac
Δ = -992-4·7·92
Δ = 7225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{7225}=85$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-99)-85}{2*7}=\frac{14}{14}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-99)+85}{2*7}=\frac{184}{14}
=13+1/7
$