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4x^2+6x=9x^2-15x
We move all terms to the left:
4x^2+6x-(9x^2-15x)=0
We get rid of parentheses
4x^2-9x^2+6x+15x=0
We add all the numbers together, and all the variables
-5x^2+21x=0
a = -5; b = 21; c = 0;
Δ = b2-4ac
Δ = 212-4·(-5)·0
Δ = 441
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{441}=21$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(21)-21}{2*-5}=\frac{-42}{-10} =4+1/5 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+21}{2*-5}=\frac{0}{-10} =0 $
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