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(3+5x)(2-3x)=12-30x
We move all terms to the left:
(3+5x)(2-3x)-(12-30x)=0
We add all the numbers together, and all the variables
(5x+3)(-3x+2)-(-30x+12)=0
We get rid of parentheses
(5x+3)(-3x+2)+30x-12=0
We multiply parentheses ..
(-15x^2+10x-9x+6)+30x-12=0
We get rid of parentheses
-15x^2+10x-9x+30x+6-12=0
We add all the numbers together, and all the variables
-15x^2+31x-6=0
a = -15; b = 31; c = -6;
Δ = b2-4ac
Δ = 312-4·(-15)·(-6)
Δ = 601
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{-(31)-\sqrt{601}}{2*-15}=\frac{-31-\sqrt{601}}{-30} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(31)+\sqrt{601}}{2*-15}=\frac{-31+\sqrt{601}}{-30} $
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