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7x^2=4x+9
We move all terms to the left:
7x^2-(4x+9)=0
We get rid of parentheses
7x^2-4x-9=0
a = 7; b = -4; c = -9;
Δ = b2-4ac
Δ = -42-4·7·(-9)
Δ = 268
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{268}=\sqrt{4*67}=\sqrt{4}*\sqrt{67}=2\sqrt{67}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-2\sqrt{67}}{2*7}=\frac{4-2\sqrt{67}}{14} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+2\sqrt{67}}{2*7}=\frac{4+2\sqrt{67}}{14} $
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