10x^2-3=14x

Solution for 10x^2-3=14x equation:

10x^2-3=14x

We move all terms to the left:

10x^2-3-(14x)=0

a = 10; b = -14; c = -3;
Δ = b2-4ac
Δ = -142-4·10·(-3)
Δ = 316
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:

$\sqrt{\Delta}=\sqrt{316}=\sqrt{4*79}=\sqrt{4}*\sqrt{79}=2\sqrt{79}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{79}}{2*10}=\frac{14-2\sqrt{79}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{79}}{2*10}=\frac{14+2\sqrt{79}}{20}
$