28x^2+1=13x+7

Solution for 28x^2+1=13x+7 equation:

28x^2+1=13x+7

We move all terms to the left:

28x^2+1-(13x+7)=0

We get rid of parentheses

28x^2-13x-7+1=0

We add all the numbers together, and all the variables

28x^2-13x-6=0

a = 28; b = -13; c = -6;
Δ = b2-4ac
Δ = -132-4·28·(-6)
Δ = 841
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{841}=29$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-29}{2*28}=\frac{-16}{56}
=-2/7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+29}{2*28}=\frac{42}{56}
=3/4
$