2x^2-5x+3=9x+15

Solution for 2x^2-5x+3=9x+15 equation:

2x^2-5x+3=9x+15

We move all terms to the left:

2x^2-5x+3-(9x+15)=0

We get rid of parentheses

2x^2-5x-9x-15+3=0

We add all the numbers together, and all the variables

2x^2-14x-12=0

a = 2; b = -14; c = -12;
Δ = b2-4ac
Δ = -142-4·2·(-12)
Δ = 292
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:

$\sqrt{\Delta}=\sqrt{292}=\sqrt{4*73}=\sqrt{4}*\sqrt{73}=2\sqrt{73}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{73}}{2*2}=\frac{14-2\sqrt{73}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{73}}{2*2}=\frac{14+2\sqrt{73}}{4}
$