5x2=10x+3

Solution for 5x2=10x+3 equation:

5x^2=10x+3

We move all terms to the left:

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

We get rid of parentheses

5x^2-10x-3=0

a = 5; b = -10; c = -3;
Δ = b2-4ac
Δ = -102-4·5·(-3)
Δ = 160
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:

$\sqrt{\Delta}=\sqrt{160}=\sqrt{16*10}=\sqrt{16}*\sqrt{10}=4\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-4\sqrt{10}}{2*5}=\frac{10-4\sqrt{10}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+4\sqrt{10}}{2*5}=\frac{10+4\sqrt{10}}{10}
$