5x^2-10=4x+3

Solution for 5x^2-10=4x+3 equation:

5x^2-10=4x+3

We move all terms to the left:

5x^2-10-(4x+3)=0

We get rid of parentheses

5x^2-4x-3-10=0

We add all the numbers together, and all the variables

5x^2-4x-13=0

a = 5; b = -4; c = -13;
Δ = b2-4ac
Δ = -42-4·5·(-13)
Δ = 276
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:

$\sqrt{\Delta}=\sqrt{276}=\sqrt{4*69}=\sqrt{4}*\sqrt{69}=2\sqrt{69}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-2\sqrt{69}}{2*5}=\frac{4-2\sqrt{69}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+2\sqrt{69}}{2*5}=\frac{4+2\sqrt{69}}{10}
$