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6x^2+5x-7=4
We move all terms to the left:
6x^2+5x-7-(4)=0
We add all the numbers together, and all the variables
6x^2+5x-11=0
a = 6; b = 5; c = -11;
Δ = b2-4ac
Δ = 52-4·6·(-11)
Δ = 289
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$\sqrt{\Delta}=\sqrt{289}=17$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-17}{2*6}=\frac{-22}{12} =-1+5/6 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+17}{2*6}=\frac{12}{12} =1 $
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