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2x+5=3x*3x+2x-7
We move all terms to the left:
2x+5-(3x*3x+2x-7)=0
We add all the numbers together, and all the variables
2x-(2x+3x*3x-7)+5=0
We get rid of parentheses
2x-2x-3x*3x+7+5=0
We add all the numbers together, and all the variables
-3x*3x+12=0
Wy multiply elements
-9x^2+12=0
a = -9; b = 0; c = +12;
Δ = b2-4ac
Δ = 02-4·(-9)·12
Δ = 432
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{432}=\sqrt{144*3}=\sqrt{144}*\sqrt{3}=12\sqrt{3}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{3}}{2*-9}=\frac{0-12\sqrt{3}}{-18} =-\frac{12\sqrt{3}}{-18} =-\frac{2\sqrt{3}}{-3} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{3}}{2*-9}=\frac{0+12\sqrt{3}}{-18} =\frac{12\sqrt{3}}{-18} =\frac{2\sqrt{3}}{-3} $
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