x^2+5.1x=6.57

Solution for x^2+5.1x=6.57 equation:

x^2+5.1x=6.57

We move all terms to the left:

x^2+5.1x-(6.57)=0

We add all the numbers together, and all the variables

x^2+5.1x-6.57=0

a = 1; b = 5.1; c = -6.57;
Δ = b2-4ac
Δ = 5.12-4·1·(-6.57)
Δ = 52.29
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{-(5.1)-\sqrt{52.29}}{2*1}=\frac{-5.1-\sqrt{52.29}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5.1)+\sqrt{52.29}}{2*1}=\frac{-5.1+\sqrt{52.29}}{2}
$