8u^2-6u=5

Solution for 8u^2-6u=5 equation:

8u^2-6u=5

We move all terms to the left:

8u^2-6u-(5)=0

a = 8; b = -6; c = -5;
Δ = b2-4ac
Δ = -62-4·8·(-5)
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-14}{2*8}=\frac{-8}{16}
=-1/2
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+14}{2*8}=\frac{20}{16}
=1+1/4
$