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8x(14x+4)=180
We move all terms to the left:
8x(14x+4)-(180)=0
We multiply parentheses
112x^2+32x-180=0
a = 112; b = 32; c = -180;
Δ = b2-4ac
Δ = 322-4·112·(-180)
Δ = 81664
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{81664}=\sqrt{256*319}=\sqrt{256}*\sqrt{319}=16\sqrt{319}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(32)-16\sqrt{319}}{2*112}=\frac{-32-16\sqrt{319}}{224} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(32)+16\sqrt{319}}{2*112}=\frac{-32+16\sqrt{319}}{224} $
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