8x^2+11x=172

Solution for 8x^2+11x=172 equation:

8x^2+11x=172

We move all terms to the left:

8x^2+11x-(172)=0

a = 8; b = 11; c = -172;
Δ = b2-4ac
Δ = 112-4·8·(-172)
Δ = 5625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5625}=75$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-75}{2*8}=\frac{-86}{16}
=-5+3/8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+75}{2*8}=\frac{64}{16}
=4
$