10x^2+6x=5

Solution for 10x^2+6x=5 equation:

10x^2+6x=5

We move all terms to the left:

10x^2+6x-(5)=0

a = 10; b = 6; c = -5;
Δ = b2-4ac
Δ = 62-4·10·(-5)
Δ = 236
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{236}=\sqrt{4*59}=\sqrt{4}*\sqrt{59}=2\sqrt{59}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{59}}{2*10}=\frac{-6-2\sqrt{59}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{59}}{2*10}=\frac{-6+2\sqrt{59}}{20}
$