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2x^2+7x-2=11
We move all terms to the left:
2x^2+7x-2-(11)=0
We add all the numbers together, and all the variables
2x^2+7x-13=0
a = 2; b = 7; c = -13;
Δ = b2-4ac
Δ = 72-4·2·(-13)
Δ = 153
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{153}=\sqrt{9*17}=\sqrt{9}*\sqrt{17}=3\sqrt{17}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-3\sqrt{17}}{2*2}=\frac{-7-3\sqrt{17}}{4} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+3\sqrt{17}}{2*2}=\frac{-7+3\sqrt{17}}{4} $
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