5x^2-8=3x-6

Solution for 5x^2-8=3x-6 equation:

5x^2-8=3x-6

We move all terms to the left:

5x^2-8-(3x-6)=0

We get rid of parentheses

5x^2-3x+6-8=0

We add all the numbers together, and all the variables

5x^2-3x-2=0

a = 5; b = -3; c = -2;
Δ = b2-4ac
Δ = -32-4·5·(-2)
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-7}{2*5}=\frac{-4}{10}
=-2/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+7}{2*5}=\frac{10}{10}
=1
$