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5x^2-x+5=6x+3
We move all terms to the left:
5x^2-x+5-(6x+3)=0
We add all the numbers together, and all the variables
5x^2-1x-(6x+3)+5=0
We get rid of parentheses
5x^2-1x-6x-3+5=0
We add all the numbers together, and all the variables
5x^2-7x+2=0
a = 5; b = -7; c = +2;
Δ = b2-4ac
Δ = -72-4·5·2
Δ = 9
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$\sqrt{\Delta}=\sqrt{9}=3$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-3}{2*5}=\frac{4}{10} =2/5 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+3}{2*5}=\frac{10}{10} =1 $
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