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3x^2-5x+3=10x
We move all terms to the left:
3x^2-5x+3-(10x)=0
We add all the numbers together, and all the variables
3x^2-15x+3=0
a = 3; b = -15; c = +3;
Δ = b2-4ac
Δ = -152-4·3·3
Δ = 189
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{189}=\sqrt{9*21}=\sqrt{9}*\sqrt{21}=3\sqrt{21}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-3\sqrt{21}}{2*3}=\frac{15-3\sqrt{21}}{6} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+3\sqrt{21}}{2*3}=\frac{15+3\sqrt{21}}{6} $
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