8x^2-3=5x

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

8x^2-3=5x

We move all terms to the left:

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

a = 8; b = -5; c = -3;
Δ = b2-4ac
Δ = -52-4·8·(-3)
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-11}{2*8}=\frac{-6}{16}
=-3/8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+11}{2*8}=\frac{16}{16}
=1
$