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7x^2+4x=100
We move all terms to the left:
7x^2+4x-(100)=0
a = 7; b = 4; c = -100;
Δ = b2-4ac
Δ = 42-4·7·(-100)
Δ = 2816
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{2816}=\sqrt{256*11}=\sqrt{256}*\sqrt{11}=16\sqrt{11}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-16\sqrt{11}}{2*7}=\frac{-4-16\sqrt{11}}{14} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+16\sqrt{11}}{2*7}=\frac{-4+16\sqrt{11}}{14} $
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