x^2-5.3x=4.2

Solution for x^2-5.3x=4.2 equation:

x^2-5.3x=4.2

We move all terms to the left:

x^2-5.3x-(4.2)=0

We add all the numbers together, and all the variables

x^2-5.3x-4.2=0

a = 1; b = -5.3; c = -4.2;
Δ = b2-4ac
Δ = -5.32-4·1·(-4.2)
Δ = 44.89
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{-(-5.3)-\sqrt{44.89}}{2*1}=\frac{5.3-\sqrt{44.89}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5.3)+\sqrt{44.89}}{2*1}=\frac{5.3+\sqrt{44.89}}{2}
$