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52x+4x^2=69
We move all terms to the left:
52x+4x^2-(69)=0
a = 4; b = 52; c = -69;
Δ = b2-4ac
Δ = 522-4·4·(-69)
Δ = 3808
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{3808}=\sqrt{16*238}=\sqrt{16}*\sqrt{238}=4\sqrt{238}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(52)-4\sqrt{238}}{2*4}=\frac{-52-4\sqrt{238}}{8} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(52)+4\sqrt{238}}{2*4}=\frac{-52+4\sqrt{238}}{8} $
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