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3x-4x^2=9x-59
We move all terms to the left:
3x-4x^2-(9x-59)=0
We get rid of parentheses
-4x^2+3x-9x+59=0
We add all the numbers together, and all the variables
-4x^2-6x+59=0
a = -4; b = -6; c = +59;
Δ = b2-4ac
Δ = -62-4·(-4)·59
Δ = 980
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{980}=\sqrt{196*5}=\sqrt{196}*\sqrt{5}=14\sqrt{5}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-14\sqrt{5}}{2*-4}=\frac{6-14\sqrt{5}}{-8} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+14\sqrt{5}}{2*-4}=\frac{6+14\sqrt{5}}{-8} $
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