5x^2-7x=-6x+45

Solution for 5x^2-7x=-6x+45 equation:

5x^2-7x=-6x+45

We move all terms to the left:

5x^2-7x-(-6x+45)=0

We get rid of parentheses

5x^2-7x+6x-45=0

We add all the numbers together, and all the variables

5x^2-1x-45=0

a = 5; b = -1; c = -45;
Δ = b2-4ac
Δ = -12-4·5·(-45)
Δ = 901
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-\sqrt{901}}{2*5}=\frac{1-\sqrt{901}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{901}}{2*5}=\frac{1+\sqrt{901}}{10}
$