237=1.55x^2-5.1x+197

Solution for 237=1.55x^2-5.1x+197 equation:

237=1.55x^2-5.1x+197

We move all terms to the left:

237-(1.55x^2-5.1x+197)=0

We get rid of parentheses

-1.55x^2+5.1x-197+237=0

We add all the numbers together, and all the variables

-1.55x^2+5.1x+40=0

a = -1.55; b = 5.1; c = +40;
Δ = b2-4ac
Δ = 5.12-4·(-1.55)·40
Δ = 274.01
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{274.01}}{2*-1.55}=\frac{-5.1-\sqrt{274.01}}{-3.1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5.1)+\sqrt{274.01}}{2*-1.55}=\frac{-5.1+\sqrt{274.01}}{-3.1}
$