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7x(5x+12)=108
We move all terms to the left:
7x(5x+12)-(108)=0
We multiply parentheses
35x^2+84x-108=0
a = 35; b = 84; c = -108;
Δ = b2-4ac
Δ = 842-4·35·(-108)
Δ = 22176
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{22176}=\sqrt{144*154}=\sqrt{144}*\sqrt{154}=12\sqrt{154}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(84)-12\sqrt{154}}{2*35}=\frac{-84-12\sqrt{154}}{70} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(84)+12\sqrt{154}}{2*35}=\frac{-84+12\sqrt{154}}{70} $
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