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x^2-24x+62=-9x+6x^2
We move all terms to the left:
x^2-24x+62-(-9x+6x^2)=0
We get rid of parentheses
x^2-6x^2+9x-24x+62=0
We add all the numbers together, and all the variables
-5x^2-15x+62=0
a = -5; b = -15; c = +62;
Δ = b2-4ac
Δ = -152-4·(-5)·62
Δ = 1465
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{-(-15)-\sqrt{1465}}{2*-5}=\frac{15-\sqrt{1465}}{-10} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+\sqrt{1465}}{2*-5}=\frac{15+\sqrt{1465}}{-10} $
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