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4x(5x+2)=182
We move all terms to the left:
4x(5x+2)-(182)=0
We multiply parentheses
20x^2+8x-182=0
a = 20; b = 8; c = -182;
Δ = b2-4ac
Δ = 82-4·20·(-182)
Δ = 14624
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{14624}=\sqrt{16*914}=\sqrt{16}*\sqrt{914}=4\sqrt{914}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-4\sqrt{914}}{2*20}=\frac{-8-4\sqrt{914}}{40} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+4\sqrt{914}}{2*20}=\frac{-8+4\sqrt{914}}{40} $
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