8x2=20x+45

Solution for 8x2=20x+45 equation:

8x^2=20x+45

We move all terms to the left:

8x^2-(20x+45)=0

We get rid of parentheses

8x^2-20x-45=0

a = 8; b = -20; c = -45;
Δ = b2-4ac
Δ = -202-4·8·(-45)
Δ = 1840
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:

$\sqrt{\Delta}=\sqrt{1840}=\sqrt{16*115}=\sqrt{16}*\sqrt{115}=4\sqrt{115}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-4\sqrt{115}}{2*8}=\frac{20-4\sqrt{115}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+4\sqrt{115}}{2*8}=\frac{20+4\sqrt{115}}{16}
$