10x^2+9x=5.2

Solution for 10x^2+9x=5.2 equation:

10x^2+9x=5.2

We move all terms to the left:

10x^2+9x-(5.2)=0

We add all the numbers together, and all the variables

10x^2+9x-5.2=0

a = 10; b = 9; c = -5.2;
Δ = b2-4ac
Δ = 92-4·10·(-5.2)
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-17}{2*10}=\frac{-26}{20}
=-1+3/10
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+17}{2*10}=\frac{8}{20}
=2/5
$