10x2+13x=3

Solution for 10x2+13x=3 equation:

10x^2+13x=3

We move all terms to the left:

10x^2+13x-(3)=0

a = 10; b = 13; c = -3;
Δ = b2-4ac
Δ = 132-4·10·(-3)
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{-(13)-17}{2*10}=\frac{-30}{20}
=-1+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+17}{2*10}=\frac{4}{20}
=1/5
$