7x^2+15x=5+2x^2

Solution for 7x^2+15x=5+2x^2 equation:

7x^2+15x=5+2x^2

We move all terms to the left:

7x^2+15x-(5+2x^2)=0

We get rid of parentheses

7x^2-2x^2+15x-5=0

We add all the numbers together, and all the variables

5x^2+15x-5=0

a = 5; b = 15; c = -5;
Δ = b2-4ac
Δ = 152-4·5·(-5)
Δ = 325
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:

$\sqrt{\Delta}=\sqrt{325}=\sqrt{25*13}=\sqrt{25}*\sqrt{13}=5\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-5\sqrt{13}}{2*5}=\frac{-15-5\sqrt{13}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+5\sqrt{13}}{2*5}=\frac{-15+5\sqrt{13}}{10}
$