8x^2+59x=40

Solution for 8x^2+59x=40 equation:

8x^2+59x=40

We move all terms to the left:

8x^2+59x-(40)=0

a = 8; b = 59; c = -40;
Δ = b2-4ac
Δ = 592-4·8·(-40)
Δ = 4761
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4761}=69$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(59)-69}{2*8}=\frac{-128}{16}
=-8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(59)+69}{2*8}=\frac{10}{16}
=5/8
$