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4X(5X-7)=32
We move all terms to the left:
4X(5X-7)-(32)=0
We multiply parentheses
20X^2-28X-32=0
a = 20; b = -28; c = -32;
Δ = b2-4ac
Δ = -282-4·20·(-32)
Δ = 3344
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}$$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{3344}=\sqrt{16*209}=\sqrt{16}*\sqrt{209}=4\sqrt{209}$$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-28)-4\sqrt{209}}{2*20}=\frac{28-4\sqrt{209}}{40} $$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-28)+4\sqrt{209}}{2*20}=\frac{28+4\sqrt{209}}{40} $
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