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9(5x^2)+8(3-5x)-23=3(2x-1)-7x
We move all terms to the left:
9(5x^2)+8(3-5x)-23-(3(2x-1)-7x)=0
We add all the numbers together, and all the variables
95x^2+8(-5x+3)-(3(2x-1)-7x)-23=0
We multiply parentheses
95x^2-40x-(3(2x-1)-7x)+24-23=0
We calculate terms in parentheses: -(3(2x-1)-7x), so:We add all the numbers together, and all the variables
3(2x-1)-7x
We add all the numbers together, and all the variables
-7x+3(2x-1)
We multiply parentheses
-7x+6x-3
We add all the numbers together, and all the variables
-1x-3
Back to the equation:
-(-1x-3)
95x^2-40x-(-1x-3)+1=0
We get rid of parentheses
95x^2-40x+1x+3+1=0
We add all the numbers together, and all the variables
95x^2-39x+4=0
a = 95; b = -39; c = +4;
Δ = b2-4ac
Δ = -392-4·95·4
Δ = 1
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{1}=1x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-39)-1}{2*95}=\frac{38}{190} =1/5x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-39)+1}{2*95}=\frac{40}{190} =4/19
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