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7x-9x^2=5x-8
We move all terms to the left:
7x-9x^2-(5x-8)=0
We get rid of parentheses
-9x^2+7x-5x+8=0
We add all the numbers together, and all the variables
-9x^2+2x+8=0
a = -9; b = 2; c = +8;
Δ = b2-4ac
Δ = 22-4·(-9)·8
Δ = 292
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{292}=\sqrt{4*73}=\sqrt{4}*\sqrt{73}=2\sqrt{73}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{73}}{2*-9}=\frac{-2-2\sqrt{73}}{-18} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{73}}{2*-9}=\frac{-2+2\sqrt{73}}{-18} $
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