5x^2-3=10x+12

Solution for 5x^2-3=10x+12 equation:

5x^2-3=10x+12

We move all terms to the left:

5x^2-3-(10x+12)=0

We get rid of parentheses

5x^2-10x-12-3=0

We add all the numbers together, and all the variables

5x^2-10x-15=0

a = 5; b = -10; c = -15;
Δ = b2-4ac
Δ = -102-4·5·(-15)
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-20}{2*5}=\frac{-10}{10}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+20}{2*5}=\frac{30}{10}
=3
$