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-5x(2x-3)+4x=-3x+6
We move all terms to the left:
-5x(2x-3)+4x-(-3x+6)=0
We add all the numbers together, and all the variables
4x-5x(2x-3)-(-3x+6)=0
We multiply parentheses
-10x^2+4x+15x-(-3x+6)=0
We get rid of parentheses
-10x^2+4x+15x+3x-6=0
We add all the numbers together, and all the variables
-10x^2+22x-6=0
a = -10; b = 22; c = -6;
Δ = b2-4ac
Δ = 222-4·(-10)·(-6)
Δ = 244
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{244}=\sqrt{4*61}=\sqrt{4}*\sqrt{61}=2\sqrt{61}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(22)-2\sqrt{61}}{2*-10}=\frac{-22-2\sqrt{61}}{-20} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(22)+2\sqrt{61}}{2*-10}=\frac{-22+2\sqrt{61}}{-20} $
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