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3x(2-5x)-(x-3)=0
We add all the numbers together, and all the variables
3x(-5x+2)-(x-3)=0
We multiply parentheses
-15x^2+6x-(x-3)=0
We get rid of parentheses
-15x^2+6x-x+3=0
We add all the numbers together, and all the variables
-15x^2+5x+3=0
a = -15; b = 5; c = +3;
Δ = b2-4ac
Δ = 52-4·(-15)·3
Δ = 205
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{-(5)-\sqrt{205}}{2*-15}=\frac{-5-\sqrt{205}}{-30} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{205}}{2*-15}=\frac{-5+\sqrt{205}}{-30} $
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