5x^2-3x=10

Solution for 5x^2-3x=10 equation:

5x^2-3x=10

We move all terms to the left:

5x^2-3x-(10)=0

a = 5; b = -3; c = -10;
Δ = b2-4ac
Δ = -32-4·5·(-10)
Δ = 209
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{-(-3)-\sqrt{209}}{2*5}=\frac{3-\sqrt{209}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{209}}{2*5}=\frac{3+\sqrt{209}}{10}
$