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5x*5x-16=4x*4x-6x
We move all terms to the left:
5x*5x-16-(4x*4x-6x)=0
We add all the numbers together, and all the variables
5x*5x-(-6x+4x*4x)-16=0
Wy multiply elements
25x^2-(-6x+4x*4x)-16=0
We get rid of parentheses
25x^2+6x-4x*4x-16=0
Wy multiply elements
25x^2-16x^2+6x-16=0
We add all the numbers together, and all the variables
9x^2+6x-16=0
a = 9; b = 6; c = -16;
Δ = b2-4ac
Δ = 62-4·9·(-16)
Δ = 612
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{612}=\sqrt{36*17}=\sqrt{36}*\sqrt{17}=6\sqrt{17}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-6\sqrt{17}}{2*9}=\frac{-6-6\sqrt{17}}{18} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6\sqrt{17}}{2*9}=\frac{-6+6\sqrt{17}}{18} $
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