x/2+1=7x^2/2

Solution for x/2+1=7x^2/2 equation:

x/2+1=7x^2/2

We move all terms to the left:

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

We get rid of parentheses

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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

-7x^2+x+2=0

a = -7; b = 1; c = +2;
Δ = b2-4ac
Δ = 12-4·(-7)·2
Δ = 57
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{-(1)-\sqrt{57}}{2*-7}=\frac{-1-\sqrt{57}}{-14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{57}}{2*-7}=\frac{-1+\sqrt{57}}{-14}
$