Move right part of the equation to left part with negative sign.
The equation is transformed from 2x2−3x+15=11x−5 to (−11x+5)+(2x2−3x+15)=0 This equation is of the form ax2+bx+c=0 A quadratic equation can be solved using the discriminant The roots of the quadratic equation: x1=2aD−b x2=2a−D−b where D=b2−4ac is the discriminant. Because a=2 b=−14 c=20 , then D=b2−4ac= (−1)2⋅4⋅20+(−14)2=36 Because D > 0, then the equation has two roots. x1=2a(−b+D) x2=2a(−b−D) or x1=5 Simplify x2=2 Simplify
Vieta's Theorem
rewrite the equation 2x2−3x+15=11x−5 of ax2+bx+c=0 as reduced quadratic equation x2+abx+ac=0 x2−7x+10=0 px+x2+q=0 where p=ab p=−7 q=ac q=10 Vieta Formulas x1+x2=−p x1x2=q x1+x2=7 x1x2=10