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3x-5(x-3)x=-5+2x-4
We move all terms to the left:
3x-5(x-3)x-(-5+2x-4)=0
We add all the numbers together, and all the variables
3x-5(x-3)x-(2x-9)=0
We multiply parentheses
-5x^2+3x+15x-(2x-9)=0
We get rid of parentheses
-5x^2+3x+15x-2x+9=0
We add all the numbers together, and all the variables
-5x^2+16x+9=0
a = -5; b = 16; c = +9;
Δ = b2-4ac
Δ = 162-4·(-5)·9
Δ = 436
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{436}=\sqrt{4*109}=\sqrt{4}*\sqrt{109}=2\sqrt{109}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-2\sqrt{109}}{2*-5}=\frac{-16-2\sqrt{109}}{-10} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+2\sqrt{109}}{2*-5}=\frac{-16+2\sqrt{109}}{-10} $
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