5x^2-28x=-10

Solution for 5x^2-28x=-10 equation:

5x^2-28x=-10

We move all terms to the left:

5x^2-28x-(-10)=0

We add all the numbers together, and all the variables

5x^2-28x+10=0

a = 5; b = -28; c = +10;
Δ = b2-4ac
Δ = -282-4·5·10
Δ = 584
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:

$\sqrt{\Delta}=\sqrt{584}=\sqrt{4*146}=\sqrt{4}*\sqrt{146}=2\sqrt{146}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-28)-2\sqrt{146}}{2*5}=\frac{28-2\sqrt{146}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-28)+2\sqrt{146}}{2*5}=\frac{28+2\sqrt{146}}{10}
$