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18-4x-7x^2=0
a = -7; b = -4; c = +18;
Δ = b2-4ac
Δ = -42-4·(-7)·18
Δ = 520
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{520}=\sqrt{4*130}=\sqrt{4}*\sqrt{130}=2\sqrt{130}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-2\sqrt{130}}{2*-7}=\frac{4-2\sqrt{130}}{-14} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+2\sqrt{130}}{2*-7}=\frac{4+2\sqrt{130}}{-14} $
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