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(8x-5)(2x-3)=0
We multiply parentheses ..
(+16x^2-24x-10x+15)=0
We get rid of parentheses
16x^2-24x-10x+15=0
We add all the numbers together, and all the variables
16x^2-34x+15=0
a = 16; b = -34; c = +15;
Δ = b2-4ac
Δ = -342-4·16·15
Δ = 196
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{196}=14$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-34)-14}{2*16}=\frac{20}{32} =5/8 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-34)+14}{2*16}=\frac{48}{32} =1+1/2 $
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