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3x^2+4x=7-2x^2+9x=7
We move all terms to the left:
3x^2+4x-(7-2x^2+9x)=0
We get rid of parentheses
3x^2+2x^2-9x+4x-7=0
We add all the numbers together, and all the variables
5x^2-5x-7=0
a = 5; b = -5; c = -7;
Δ = b2-4ac
Δ = -52-4·5·(-7)
Δ = 165
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-\sqrt{165}}{2*5}=\frac{5-\sqrt{165}}{10} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{165}}{2*5}=\frac{5+\sqrt{165}}{10} $
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