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5x(-4-3x+5)=-3
We move all terms to the left:
5x(-4-3x+5)-(-3)=0
We add all the numbers together, and all the variables
5x(-3x+1)-(-3)=0
We add all the numbers together, and all the variables
5x(-3x+1)+3=0
We multiply parentheses
-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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